Bequeathed Power

Before a character dies or before performing a Heroic Sacrifice, they give all of or at least some of their power to the person they have the closest relationship to. Expect the receiver to say that they didn't have to do this while sobbing. The character who gave this power is often a mentor of the receiver.

Subtrope of Super Empowering, however the deceased person isn't really known for this ability, and the fact that he has this power is in some cases never brought up before he died. The receiver usually isn't a Power Parasite or the possessor of a Cannibalism Superpower, though.

As a Death Trope, Spoilers ahead may be unmarked. Beware.

Examples of Bequeathed Power include:

Anime and Manga

In Beet the Vandel Buster, a whole team of busters pass their saiga on to Beet before their (apparent) Heroic Sacrifice.
In Hunter X Hunter, Pakunoda gets afflicted with a curse that causes her to die if she uses her powers. She makes her way back to the organization she works for and uses her powers one last time, to insert what she knows about her attacker into their memories so they all have detailed information about this assailant.
In The Lucifer and Biscuit Hammer, Hangetsu Shinome uses his wish as one of the Animal Knights to bequeath his phenomenal martial arts skills to Amamiya Yuuhi when he recieves a mortal blow in battle.
In S-Cry-ed, Cherise Adjani's sole power is to allow whoever she loves most to be resurrected from any sort of death at the cost of her own life.
In Yu Yu Hakusho close to the end of the Dark Tournament Genkai gives Yusuke her Spirit Wave Power before she sacrifices herself to Toguro. She had an Unexplained Recovery later though.
Scar from Fullmetal Alchemist got his alchemy seals from his brother in a case of Blessed with Suck.

Comic Books

In Savage Dragon, the superhero Mighty Man works in this manner. The most common version is nurse Ann Stevens who was unwittingly given the Mighty Man power while treating the previous, dying host.
Similar to Animorphs is the Power Pack comic. The kids here also get their powers from a dying alien.
The Green Lantern ring was given to Hal Jordan by a dying alien.
In A Distant Soil, the original Rieken attempts to given Seren his memories as he is dying. This goes wrong, and Seren actually becomes Rieken in all but face and psychic ability.

Fan Works

In the Axis Powers Hetalia After the End fanfic Gutters, Denmark performs a Heroic Sacrifice in order to let Sealand escape to safety. Through a mechanism that lets his body live three more days he bequeaths the remaining arable land of Denmark to Sealand, transforming him into a real nation.

Film

In Transformers: Revenge of the Fallen, the dying Jetfire insists that Optimus repair and augment himself with Jetfire's jet engines and other parts for his fight with the Fallen.
Sgt. Kabukiman N.Y.P.D.: An dying old Japanese man transfers the power of Kabuki to a cop.
In the Transformers: The Movie, Optimus Prime gives the Autobots Matrix of Leadership to Ultra Magnus. It later goes to Hot Rod.

Literature

In Stone of Tears, each Sister of Light, if she fails to convince a person with the gift to come train with them, passes her life force to another, so that when the second one (or third one) attempts, she has stronger Mind Control powers to add to her arguments.
In Malazan Book of the Fallen this is how Quick Ben became so powerful. A cabal of mages fled into the desert to escape pursuit by the Malazan army that conquered their city. When they run low on water, the older, physically weakest but magically strongest members of the group transferred their power and life force to the younger members. When the Malazan soldiers finally caught up to them, only the youngest member of the cabal still lived and he now possessed the combined magic and knowledge of the entire cabal. He adopted the name Quick Ben and joined the newly formed Bridgeburners as their first cadre mage.
In Animorphs the protagonist and his friends all get their power from a dying alien.
In Sourcery, a wizard is about to die (Death is standing by, waiting) and gives his staff to his newborn son... then projects himself and his wizard powers into it. This causes no end of problems for the kid as he grows up.
In Bright Shadows by Avi, the book starts with a poor kitchen girl running into a dying man in the castle that everyone else is ignoring. He gives her the last five wishes of legend in the land right before he dies.

Live-Action TV

In Angel, Doyle passes on his prophetic visions to Cordelia via kiss, just before going off to heroically sacrifice himself.

Oral Tradition, Folklore, Myths and Legends

In Russian Mythology and Tales, Ilya Muromets receives his Super Strength from the dying Svyatogor.
Older Than Feudalism actually. In The Bible, Elijah promises to bequeath his power to his disciple Elisha if Elisha sees Elijah Ascend to a Higher Plane of Existence. Elisha does indeed witness this and inherits Elijah's mantel—figuratively and literally—as Elijah is taken into Heaven.

Tabletop Games

In Birthright power of a dying scion's Bloodline, unless usurped, goes to the pre-designated heir.

Web Comics

In Spinnerette, this is implied to be how Tiger got his powers (though we never see the actual moment of transfer).

Video Games

In Final Fantasy VIII, Ultimecia hands her powers to Edea in the past after her Time Compression plot fails. As a timey wimey bally detail, due to the unrolling of the time compression where Ultimecia has the power of all the sorcerers in her future, Edea ends up receiving the power of all Sorcerers in history.
- Final Fantasy V: Galuf gives his power to his granddaughter, Krylie, after giving his all to fight off the newly-restored Exdeath.
In Zenonia 4 The hero lives in a typical RPG village with his dad. However he soon discovers that he is actually trapped in a fantasy realty inside his mind thankfully his future self gives him all his powers to Set Right What Once Went Wrong by giving him all his powers.
In Pokémon, the move Healing Wish will faint the user immediately; the Pokemon that takes its place is healed to full capacity.
Chapter 10 of Magical Girl Lyrical Nanoha A's Portable: The Gears of Destiny ends with Stern and Levi handing all their remaining energy over to a protesting Lord Dearche after their battle with the Unbreakable Darkness left them nearly dead. For extra irony points, Lord Dearche is characterized as someone who only desires power, but now that she has that power, she can only scream in anguish after having lost her loyal retainers.