Law of Conservation of Normality

No matter what else gets changed, and no matter how irreversible those changes are, basic societal practices and mores will remain in sync with the culture the work is written in.

Freed from the strictures of anything resembling 'volumes' or 'episodes', many webcomic authors enjoy writing 'big' plots. Big, sprawling, possibly-never-ending Kudzu Plots that spawn two new plot points for every one resolved, and leave the characters changed forever! There's no need for Snap Back when any new readers can just read the archives to get up to date!

On the other hand, many of the same authors enjoy having characters they can identify with. And they like having a setting close enough to the modern day that they can reference current events. These things can be problematic when any given arc has enough mad, grotesque or visionary events to render the cast insane and the world unrecognizable.

The solution? Everything is mutable, except for the vicissitudes of life that everybody seems to face. For example: Imagine a David R. Rand. He's a normal guy, he works at a 7-11 and goes to college. One day, the Devil steals his soul! Furious, David astrally projects himself into the body of a Fungus from Yuggoth and battles the Devil in a devastating fight that levels Denver. Defeated, the Devil spitefully cracks open the gates of hell, releasing a plague of flesh-devouring ghouls, and retreats.

The next day, David is still a tentacled alien, and Denver is still levelled, and the Devil is still at large -- but Dave still has to drag himself across those ghoul-haunted streets to the 7-11 or there will be hell to pay. And has he really considered what his girlfriend is going to think of his new appearance?

Similar to Reed Richards Is Useless, but sillier, and goes beyond socio-economic issues. This is the standard method of keeping Planet Eris from becoming totally incomprehensible.

Compare Weirdness Censor. Contrast Superman Stays Out of Gotham.

Anime

 * Bakemonogatari lives and breathes this trope. In fact, some episodes focus so heavily on the mundane aspects of Koyomi and Senjogahara's lives and relationship that it's possible to forget that he's an ex-vampire and she was once rendered weightless by a crab god.
 * Hei in Darker Than Black becomes more the Ridiculously Average Guy the more his masked persona engages in feats of Over the Top badassery. He dispenses with this after the breaking of the masquerade, but instead there are more scenes of the Muggle characters' working days.

Comic Books

 * Spider-Man invented this.
 * Astro City refines this to a fine art. An early issue had a recent immigrant to the town (from Chicago) witness to an attack by a gigantic storm elemental. Heading to the roof to watch the fight between the monster and all of the town's superheroes, he sees a bunch of the people in his building have gathered. When he asks one woman where her kids are, she tells him that they're working on their homework. Since if the city isn't destroyed, there'll still be school tomorrow. This almost terrifies him into leaving town the next day, but when he sees how quickly the place is cleaned up and how everyone pitches in, it charms him into staying.
 * And the story "Newcomers" reveals that this isn't the case for all new arrivals - a fair few just can't take it and will go somewhere else. There are superheroes and villains in other cities, but Astro City is just an exceptional Weirdness Magnet.
 * Right after the end of DC Comics' Our Worlds at War crossover event, the World Trade Centers were destroyed. Superman was depicted as being profoundly moved by 9/11. So a few thousand people being killed by terrorists is more disturbing to Superman than an interplanetary war with the living embodiment of entropy who destroyed "countless" other planets just on his way to Earth. Over eight million Earthlings were confirmed dead.
 * 9/11 also happened in the Marvel universe. The difference being that a good deal of Marvel's heroes actually live in New York. Despite the dozen or so heroes--yes, including Reed Richards--being there after the Towers collapsed, none of them were able to stop the first plane. That's somewhat reasonable, since it was a surprise. But no one was able to divert the second plane (despite some of the NYC resident superheroes being unambiguously strong, fast, and flight-capable enough to stop a hijacked airliner in their sleep). Or keep the Towers from collapsing.
 * And of course New York has had worst things than 9/11, from Magneto turning it into a death camp, Hydra nuking a part of it, etc.
 * It is doubtful these stories will stay in continuity for long, considering that the only far reaching consequence of them was Captain America's The Unmasking. Even then writers can always explain that the bombers had some hero-repellents and so supers couldn't do anything.
 * Subverted hard in Ex Machina, when the end of the first issue reveals that
 * Atomic Robo.

Web Comics

 * College Roomies from Hell!!! is the king of this trope. Cthulhu arises, science runs amok, supernatural armies amass for the end of all things, characters mutate and die and rise again... and not once does it give them a break in their romantic and familial hangups. Usually the reverse.
 * El Goonish Shive spends so much time on and does such a good job of the characters' personal lives that you might easily forget there has been an inter-dimensional warlord apparently trying to kill them since 2002. Of course, that's just 3 weeks in plot-time.
 * Knowledge Is Power
 * Kismetropolis
 * If CRFH!!! is King then Megatokyo is Queen; This is a version of Japan where strong AI gets incorporated into Dating Sim accessories and both Sega and Sony operate black ops divisions whilst the police ride around in Humongous Mecha fighting off zombie hordes and giant monsters. And no one sees anything unusual about this. In fact, most people barely seem to notice.
 * Yeah, but...it's Tokyo. Why would anyone see anything unusual about this?
 * The police actually arrange for Kaiju attacks and the like to happen on a regular basis, possibly to conform to pop culture expectations of Tokyo being a disaster magnet. Apparently it's good for tourism.
 * Sluggy Freelance also uses this trope heavily. You accidentally brought a man-eating alien to Earth, and after running amok for a couple weeks, it shows up at your house asking for help fitting into society? Give it a job as your secretary. A demon arrives from the Dimension of Pain to try to steal your soul each Halloween? Throw a big Halloween party advertising a real live demon as the main attraction, and charge admission. Your house is haunted by hundreds of ghosts? Try to get them to chip in on rent.
 * Fans! Ever since the Government Conspiracy gave up, people have just learned to live with, well, aliens, time travellers, sliders, and espers to the point that Wendy's now offers pails of raw meat juice in case any vampires show up. High school, apparently, is no longer taken wholesale from Archie and Mean Girls a bit different.
 * Misfile plays head games with this trope. Ash has two freaking angels living in her house, plus a third angel running around causing mischief. The plot bounces back and forth between problems in the heavenly bureaucracy, the dark influence of malevolent spirits, and the everyday issues Ash and Emily have as a result of the titular misfile.
 * The Inexplicable Adventures of Bob: Clearly, no matter how many times Generictown gets attacked by aliens or dragons or an army of unicorn-riding bigfeet, it will always settle back into being a sleepy little town where nothing ever happens.

Web Original

 * In the Paradise setting, this happens in stories set in 2009 and beyond, when the masquerade has been broken and the fact that humans have been changing into potentially gender-switched Funny Animals (though normals could not see the change) is known to the world. One of the later stories in the setting, "Family Tree", involves a family holiday get-together after the Change has become widely known. Most of the family has Changed, and the last holdout's impending Change (and the possibility of it involving gender bending) is treated as a perfectly ordinary matter.

Western Animation

 * Garfield complains about this in an episode of Garfield and Friends where he prevents an alien invasion of Earth (again). Despite having prevented the enslavement of humanity, no one saw him so Garfield has to simply resume his normal life with no reward.