Living Relic

Fish Out of Temporal Water? He's made it into delightful hors d'oeuvres.

Illyria: I've nowhere to go. My kingdom is long dead. Long dead. There's so much I don't understand. I've become overwhelmed. I'm unsure of my place.
Wesley: Your place is with the rest of your people: Dead and turned to ash.

Illyria: Perhaps... but I exist here. I must learn to walk in this world.

—Angel

Cities, countries, even civilizations rise and fall through the ocean of time, becoming myths in the millennia that follow. All their triumphs and failures becoming little more than gravel and sand beneath our feet. There is one bright spot to this though, in the form of a surviving Living Relic. Somehow, a human, computer AI, robot, or immortal homunculus has managed to survive the destruction of their home and lived to tell the tale.

Though their existence can be due to a fluke of fate, they may represent an attempt to Fling a Light Into the Future as a warning, guide, or defiant marker of their existence. All well and good, except the Living Relic is probably feeling like a Fish Out of Temporal Water at the least, and has likely been suffering a case of Survivor's Guilt. Which can get gruesome if they've been alone, awake and immortal the whole time. Quite a few Living Relics are insane because of this and become an Outside Context Villain, though a few may become sane from the boredom.

Their role in a story is likely that of giving exposition to heroes who are anywhere between months to thousands of years Late to the Party. After they finish expositing, they might ask to be killed. Or join the adventuring party. Really, it's a toss up.

Rarely, the living relic has managed to join and live among normal human civilization (or an alien equivalent) and tries to live on, sometimes successfully hiding their origins. Despite the emphasis on immortal survivors of ancient civilizations, the Living Relic isn't always ancient or immortal. A derelict in space might have the Robot Buddy shut down and get started up again by the heroes thousands of years later, or a Human Popsicle can be woken up from a sleep inducing spindle. Sometimes, they might just be the last descendant of a group of survivors.

Sub-Trope to Time Abyss. See also End of an Age and Gotterdammerung for two frequent causes. Compare Living Memory.

Examples of Living Relic include:

Anime and Manga

The Hologram of Queen Serenity in Sailor Moon.
Hohenheim in Fullmetal Alchemist.
Miyu in Mai-Otome. She mostly keeps memories of the past to herself, though.
Viral in Tengen Toppa Gurren Lagann was supposed to be this and carry a tale of victory forever after being granted immortality by Lordgenome, but victory for the beastmen there was not, presumably he becomes a Living Relic
Karla, from Record of Lodoss War is this. She hails from Kastuul, an ancient kingdom of sorcery which is implied to have once been the capital of Lodoss itself. A powerful sorceress in her own right, she survived the destruction of the magic city by infusing a mystic circlet with her soul, retaining all her memories and powers as the circlet possesses the bodies of numerous hosts over the subsequent 500 years.
End of Evangelion reveals in the penultimate scene that this was Unit 01's true purpose: since humans can't exist anywhere but Evas can, Yui reached the logical conclusion of uploading her soul into Unit 01 and become an everlasting monument. That she was used to fight Cosmic Horrors in the meantime is just a perk.

Comic Books

In the noncanonical The Incredible Hulk: The End Bruce Banner is the last sentient being on earth.
The Vision in the Ultimate Marvel line. Created millions of years ago by an alien race that saw Gah Lak Tus coming for them, he she was sent out at first as just a time capsule to record the stories of Gah Lak Tus' billions of victims. After stopping on Earth, though, her mission changed to telling other people how to fight Gah Lak Tus.
In addition, Depending on the Writer, Superman in some storylines.
Captain America. He was frozen just before the end of World War II and was revived. As the years unfold and Comic Book Time has to be applied, he seems like more and more of a relic. At first, he was revived in 1962, less than twenty years after the war ended. Since roughly ten years have supposedly past, the unofficial Retcon is that he was revived in The Nineties, which would mean he was frozen for about sixty years.
- The Ultimate Marvel version of Cap was revived in the 2000's, which would be even more jarring for someone frozen during the war.
Vandal Savage, an immortal caveman.

Film

Aughra in The Dark Crystal is the only surviving witness to the breaking of the Crystal and the creation of the Mystics/Uru and Skeksis. This is stated more explicitly in the novelization than the film.
Leeloo in the The Fifth Element is a "living weapon" whose existence is integral to averting The End of the World as We Know It. Despite an ability to absorb historical data and languages instantly, she's been in a sarcophagus for 5,000 years and thus has No Social Skills.
This was done in The Fountain, where a man who obtains some sort of immortality is the last man in existence and floats about in space all alone.
The elves in Hellboy and the Golden Army. They were dying out as a lonf-forgotten race, prompting Prince Nuada to try to destroy humanity once and for all.
"Old Man" in Logan's Run is a rare example of a Living Relic who is neither immortal nor was alive in the time before civilization collapsed. He's the son of some of the last humans to live and love naturally.
The VR librarian in the 2002 The Time Machine.
As mentioned above the film versions of Captain America were frozen during the second world war and revived several decades later. For the 90's movie version, it was about sixty years. For the recent film version, it was seventy... ouch.

Literature

The War Gods: Wencit of Rum is this, having seen The Fall of Kontovar, and the only one with any appreciable book learning from the time period.
- According to one of the short stories, he's actually a god in disguise so this may not count
Belgarath and most of the other surviving Disciples of Aldur in the Belgariad. The only ones other than the Gods who were personally present at the Cracking of the World.
Peot, the Tar-Aiym Guardian from the Alan Dean Foster novel Bloodhype, was assigned by his race to the lonely task of guarding all civilization against the Vom, only to witness his people wiping themselves out in a cataclysmic interstellar war. Five hundred thousand years later, he awakens to find himself the Last of His Kind and facing a twilight struggle against the very same Vom. It's no wonder that, after the battle is finally won, he elects to commit suicide.
Human soldiers who survive their tours in The Forever War become this. Time dilation resulting from faster-than-light travel means that after just a handful of years fighting the Taurans, they return home to find that in the real-time centuries that have passed the culture that birthed them has collapsed and made way for a new and completely alien one.
The Forsaken from the Wheel of Time series can qualify as this, as they were sealed away from the world for 3,000 years. While they do use their archaic knowledge to bring back some long-lost magic, most of the time they just pine for the old days when things were so much more convenient. Also, the Green Man is the last of the Nym; artificial sentient constructs that helped plants grow before the Breaking of the World. He'd be more than happy to talk about the old days, if his memory wasn't so full of holes.
H. Rider Haggard's She: Ayesha spends most of her time doing this to the main characters.
Robert E. Howard's Conan the Barbarian has a knack for often running into this trope.
Any High Elf still in Middle Earth in the Third Age of JRR Tolkien's legendarium fits this trope, but the prize has to go to Galadriel, who has has lost her home multiple times by The Lord of the Rings, and used the power of her Ring to make Lothlorien itself a Living Relic, since as the ages pass on The Magic Goes Away, and in the end even she has to leave. However, the oldest Elf to be still living in Middle Earth is actually Cirdan, who is implied to have been one of the Elves that awoke at the beginning of time, and intends to stay in Middle Earth making ships until the last Elf leaves.
Daetrin Haal of The Madness Season is one of these, as he is the only person old enough to remember what Earth was like before the Tyr invaded and subjugated humankind. His parents were also such, as they witnessed the fall of European civilization into the Dark Ages.
Dark Reflections Trilogy has a few characters who remembers the civilization of ancient Egypt, but most prominent example may be The Flowing Queen herself, who lived in the age when gods walked the Earth. She was stated to be much older than any form of life in the sea, so this borders on a Time Abyss.
Antrax, the titular Big Bad of the second book of The Voyage of the Jerle Shannara, is a sentient supercomputer left over from the technological age that preceded the Shannara 'verse.

Live Action TV

Star Trek: The Original Series: Ruk the android was the lone sentient survivor of his long-dead race when Dr. Corby crash-lands on his planet in the ep. "What Are Little Girls Made Of?"
In Star Trek: Voyager a backup copy of The Doctor becomes this to the two species of a planet centuries after Voyager intervened in their history. The crew stopped a "civil war" between both species, and his backup fell onto the planet, where he was reactivated and started contradicting their incomplete and revisionist vision of the incident which painted Voyager and him as Complete Monsters.
Most everyone in Red Dwarf. Lister being the Human Popsicle, Kryten the android, and Cat - the last member of a surviving population, sort of...
Millennia past, Illyria from Angel was a Demonic God-Emperor whose essence was sealed into a casket after her death. Now funneled into a frail human form, she's always a bit baffled when people don't worship her. As a classicist, she tends to talk in platitudes about The Art of War.
Lorien in Babylon 5. He was the first living being to achieve sentience in the universe along with his race and was born immortal in a time before the universe invented things like life-cycles. All of his kind had died out or went beyond the rim of galaxy in the billions of intervening years. The one thing stopping him from being an Eldritch Abomination is that he also happens to be the kindest person you will ever meet.
The Doctor in Doctor Who (from 2005 onwards, anyway), the last Time Lord (except when The Master makes his semi annual return from eternal death) with one massive case of Survivors Guilt. Understandable, as he was the one to push the metaphorical button that ended the time war and destroyed Gallifrey.
In Kyoryu Sentai Zyuranger the Rangers themselves are living relics.

Video Games

Played straight in Mass Effect. Late in the game, Shepherd encounters Vigil, a Prothean VI(dumb AI) that was tasked with control of the Conduit. It was the last voice of the Protheans and had waited 50,000 years to give one final warning.
- Some might debate this following the revelation that the Collectors are genetically and cybernetically modified and enslaved Protheans but considering how much they've changed, it's a minor complaint.
- The Rachni Queen encountered during the first game also counts. She remembers the fall of her race and was their last hope for survival. Her drones have been severed from her and driven insane; she remains the last hope of the Rachni, and you get to choose.
- Now in the upcoming Mass Effect 3, You get to thaw out a Prothean warrior who then follows your cause in a day-one DLC.
In Morrowind there a single remaining member of the Dwemer race living in the basement of a 4000 year old wizard. Sadly, he can't explain what happened to the other Dwemer when they all vanished thousands of years ago.
In Endless Ocean Blue World, you can find 3 extinct creatures, including one distinctively called "Living Fossil", but most notably, a plesiosaur.
The Weapons Master in Skylanders: Spyro's Adventure is one of these; the last Arkeyan, according to one of the story scrolls.
Elh and Béluga are the last two Paladins in Solatorobo. Their home was destroyed 300 years ago, and while they seem to fit in fairly well with present-day people (no mentions of ancient clothes or Ye Olde Butcherede Englishe, though Elh is capable of reading a little of the old runes when needed), they are definitely a little emotionally distant due to seeing so many generations grow up, grow old, and die while they remained unchanged. Baion also counts, as he woke up from suspended animation 350 years ago. While it's never stated how old he was before he was frozen, he was clearly frozen for a long time, as he's from before the Juno wiped out humanity and set the Floating Continents in the sky to give the new Caninu and Felineko a place to live while the surface of the Earth recovered from the human wars.
The Fallout series has several characters that serve as living remnants of pre-nuclear war America. Besides a number of pre-war Ghouls, prominent examples include President Eden, Mr. House, ZAX and SKYNET, the Think Tank, and Professor Calvert, all of whom are either sentient computers or Brains in a Jar of one sort or another.
Neverwinter Nights 2: The great dragon Nolalothcaragascint (usually shortened to Nolaloth) was bribed by Illefarn to destroy the King of Shadows. The King struck him down after a great battle. Illefarn transmuted his heart into crystal and bound his soul to it. Nolaloth has since been consulted by people seeking to defeat the King once and for all, first the Githyanki, then Ammon Jerro, and finally the Knight-Captain. It is the KC that Nolaloth finally asks to kill him by destroying his heart, a task complicated by the fact that the valley left by the mountain-sized dragon's crash is now populated by a pair of young black dragons.
Dark Souls has Dusk of Oolacile. You meet Dusk by rescuing her while shes trapped inside a giant crystal golem, which she must have been in for several hundred years. Her nation, Oolacile is long gone, having once been located in the Lost Woods you find Dusk in.

Western Animation

The Xyber 9 from Xyber 9: New Dawn.
The Scarecrow and the Heart of Tarkon from Galaxy Rangers were sentient weapons crafted for a long-forgotten war. Once the Scarecrow wakes up, he looks for a way back to Tarkon to continue the feud. This trope also factored into "Ghost Station" where the titular Kill Sat and its remorseful AI are the only things up from an alien civilization that presumably blew itself to bits.
Avatar: The Last Airbender has two for the price of one: Aang is the last Airbender, and his sky bison Appa is the last of his species, who were the original Airbenders.
- Aang's even referred to as a "Living relic" by Professor Zei in The Library.

Real Life

Ginkgo biloba, the plant, is the one remaining species of its entire genus after multiple worldwide extinctions - a living fossil. It has no living relatives. The only stands of it in the "wild" are speculated to have been cultivated by Chinese monks, rather than surviving on their own.
The AOL operating system.
Most bacteria. Although the typical lifespan of a single bacterium is only a few hours old, their species (every single one of them) are actually all 3 billion years old! (almost as old as the Earth itself) They also happen to be the only living things that never became or can never become extinct (natural extinction events, that is, some harmful microbes were intentionally wiped out by new medical technology recently). In fact, the only thing that can truly wipe out bacteria is a dying Sun, which right now is about halfway through its life. As a result, bacteria may eventually outlive many modern plants and animals, including humanity