The protagonists in Psyren, along with any other people who answered Nemesis Q's invitation, get transported into the future are the only humans alive in the post-apocalyptic world. On the beginning, that is - by acting on the clues about the close future they found in that time, they helped some people live through the apocalypse.
Apparently what happened in the original ending of Neon Genesis Evangelion. One episode everything is fine, the next one starts with Shinji already in Limbo.
The third Rebuild movie has a straighter example. The planet is in ruins and most of humanity has been killed off, and Shinji spends a total of fourteen years in non-aging stasis inside of a giant dormant mecha while this all happens. What makes it worse this time around, is that one of the first things Shinji finds out after he wakes up is that not only did he sleep through it (in what was probably the safest place on Earth for that entire time), his actions in the previous movie are what caused it.
Near the end of Marvel Universe - The End, Thanos has destroyed the universe. Cue Adam Warlock (who had been outside reality) showing up and demanding to know what's going on.
Thanos: Adam Warlock, only you could somehow miss the end of the universe.
In Airport 75 one of the minor characters gets drunk and sleeps through the whole drama, only waking up when it's all over.
In the original ending of Army of Darkness (changed due to Executive Meddling), the hero has to drink a specific quantity from a sleeping potion so he wakes during his era, but he miscounts and when he wakes much later than he meant to, the world's been destroyed.
Genesis II. Being accidentally trapped in a suspended animation experiment causes Dylan Hunt to miss World War III. When he wakes up, mutants are in control of the surface world.
Shaun in Shaun of the Dead gets some frozen treats at the corner store without noticing the various zombies and signs of violence. However, it helps that he's both badly hungover and dealing with Romero-style slow zombies.
One guy in the middle segment of The Signal actually went about his day without noticing anything amiss, got to the New Year's Eve party, and thought nothing of all those present being covered in blood. He actually died without noticing the big picture. For reference, the titular signal made roughly 50% of the people in the city homicidal.
The protagonist Jim of 28 Days Later who was comatose in a hospital through the initial outbreak and evacuation. He wakes up naked in an abandoned hospital and spends a while wandering around an eerily empty London, trying to figure out what happened. Then he goes into a church full of dead bodies, and meets his first zombies.
The hero in The Day of the Triffids does this, when he is stuck in hospital with his eyes bandaged after suffering an accident that leaves him temporarily unable to see. Meanwhile, a meteor storm blinds almost everyone else in the world, leaving the hero, now able to see again, as one of the relatively few people who still has his sight - which against the titular Triffids, is definitely a good thing.
In Night of the Comet, the Action Girl survives because she was making out with a co-worker in a theater's metal-walled projection booth when the comet went over. Her sister had gotten locked out of the house and crashed for the night in a metal garden shed, so also failed to witness the comet or succumb to its deadly radiations.
In Brazilian movie O Noviço Rebelde, a storm destroys a church, and protagonist Didi spends some time carrying what remained of it - the confessional. At a certain point he opens the thing... and his friend Dedé is sleeping inside!
Didi: Our church was destroyed in a storm! Dedé: I thought those were people sneezing, people coughing...
The main character of Idiocracy is a volunteer for a cryogenics program who ends up being stuck in suspended animation for 500 years, at which point he wakes up to find that civilization has turned into a real dump due to humanity breeding itself into a species of utter morons.
Woody Allen's character from Sleeper woke up 200 years after he was put to sleep to find a completely different world. One in which it was finally found out that smoking was good for you, and 200 year old VW bugs (the old model) started instantly.
Marcus Wright is seemingly executed at the beginning of Terminator Salvation, only to awaken 15 years later, during the war between humanity and Skynet.
A.I.: Artificial Intelligence: David, the main robot character and the robotic Teddy Bear run out of power trapped in a capsule underwater. They're "awakened" centuries later by sentient robots that have taken over the world after all the humans are gone.
In a joke variant, Beauregard of The Muppet Show is found still living in his janitor's closet in the new The Muppets film, having apparently never noticed that the program had been canceled or the theater abandoned. No, he wasn't necessarily asleep, just so clueless he might as well have been.
Similar to this, in Get Smart, Again, Larrabee managed to complete fail to notice that CONTROL had been disbanded for years and remained at their headquarters until Max and Hymie picked him up because he had received a presidential order to remain at his post. Note that the president who gave the order was Richard Nixon, and the movie takes place in either the last year of the Reagan administration or the first year of the first Bush administration.
The first two Planet of the Apes movies combine this with Time Dilation. The ships' crews are meant to spend time in suspended animation, but end up spending longer than they expected. Of course it's not until the end of the first movie that the hero realizes he's in this trope.
In Synecdoche, New York, an elderly Caden wakes up at the end of the film after spending an unspecified amount of time bedridden. Reentering the world, he finds the cityscape devastated and most of the people he knew dead.It's never explained what happened.
German tragicomedy Good Bye, Lenin! involves the story of Alex, a disillusioned young East German who attends a democratic rally. His mother Christine, a staunch party member and decorated school teacher, suffered a stroke as she sees Stasi officers beat and arrest him. She suffers an 8 month coma during which the USSR withdraws from East Germany and eventually both countries reunite. Alex must maintain the illusion that her beloved communist world still exists, as should she realize her world has ended, replaced with corporate advertisements, destruction of Marxist monuments, her life savings obsolete, and a horde of West German "Refugees" sins of the decadent west, she cannot survive another shock.
Darkness and Dawn is a book from 1914 where a piece of the Earth breaks away into a new moon, and releases gas that kills even more people. A man and his secretary, in a high building, only are affected enough to be put into suspended animation and they wake up a thousand years later trying to survive and find other living people.
The central characters of The Day of the Triffids who missed the meteor storm that blinded most of humanity. Bill Masen was in hospital with his eyes bandaged, Josella Playton took a sleeping pill to recover from a hangover and slept through it.
A minor character in the The Langoliers falls asleep before the airplane flies through a Negative Space Wedgie, and he doesn't wake up until the entire adventure is over and the airplane is flying home.
As a possible subtle meta-joke, the way the heavy sleeper is described could fit author Stephen King himself.
And only characters who are asleep when passing through said Wedgie remain on the plane; anyone awake goes Somewhere Else, leaving behind any inorganic matter they had on (or in) them.
The protagonist of George R. Stewart's Earth Abides spent a few weeks holed up in a cabin, delirious from a rattlesnake bite he received while in the Sierra Nevadas, when he had finally recovered enough to return to civilization he found that a world-endingplague had wiped out [almost] everyone else.
In one of the vignettes in Evolution by Stephen Baxter, a hibernating "dragon's teeth" team (intended to set up resistance cells years or decades after an invading force conquers the land) never gets relieved; the survivors wake up millennia After the End and find nothing left of civilization but feral humans, heavily eroded roads and some odd-looking, grass-covered hills.
Red Dwarf again; in one of the novels, Lister ends up stranded on an ice planet that has just been moved closer to the sun, so the glaciers are all melting. He concludes that there is nothing he can do to significantly increase his chances of survival, goes back inside, and becomes the first human to sleep through the end of an ice age.
Vernor Vinge's Marooned In Realtime: After a time-halting technology called the "bobble" is invented, a number of people enter long-term suspended animation, some by choice, some not so much. But those who get bobbled near the beginning of the 23rd century, and emerge near its end, find that something seems to have happened in-between... and there's no-one left around to answer any questions.
The titular character in The Vampire Tapestry hibernates periodically, and mentions the fear that next time he'll awaken to discover that humanity has either destroyed itself (this trope), or rendered itself inedible through cybernetics and/or genetic engineering (which would qualify as this trope for him).
Happens to an alien in Larry Niven's World of Ptavvs, when it's released from temporal stasis to discover its species has been extinct for half a billion years or so.
In the Gears of War novels Marcus and Co find a whole island that has been living in complete seclusion from the outside war since the start of the war. The war that burnt 99.9% of the world's land-mass to ash and almost led to mankind's destruction. They were quite shocked to find out all about this and the fact the war is "over".
In the Diane DuaneStar Trek novel Intellivore, the titular being eats the minds of everyone on the starship Oraidhe... except for one guy who was in a coma, and thus couldn't be eaten. This is key to the Enterprise's plan to destroy it.
Animorphs has 'The Familiar', where Jake goes to sleep one night and then wakes up ten years later, in a world where the Yeerks control the planet and everyone is a controller.
Perry Rhodan's "Terra Patrol" consisted of some of the very few people left behind when Earth went through a plot-relevant Negative Space Wedgie and most of humanity simply disappeared...virtually all of whom were deeply unconscious or otherwise in significantly altered states of mind at the time of the event. The fact that these few start out scattered all over the planet and, with most of the world's infrastructure having mysteriously shut down as well, have to find each other first in order to be able to meaningfully team up provides a major driving force for for several issues' worth of plot.
Several episodes of The Twilight Zone, most notably Burgess Meredith in "Time Enough At Last."
The title character of the short-lived Cleopatra 2525, where the title character is a stripper who wakes up in the year 2525 to discover that machines known as the "Baily" have taken over the surface. Surface humans live in villages with an early medieval level of technology and worship the Bailies. The free humans and mutants live in miles-deep shafts in the earth and must contend with general lawlessness, slave trading, crimelords, the risk of falling, and Terminator-like infiltration robots called Betrayers.
Red Dwarf protagonist Dave Lister is sentenced to eighteen months in stasis for breaching quarantine regs. He wakes up three million years later to discover the ship's crew has been wiped out...along with the rest of the human race.
This is the starting premise of Andromeda; Captain Dylan Hunt of the Systems Commonwealth is frozen in time for several centuries, and comes out of it to find that the Long Night has come and the Commonwealth has fallen. An unusual variation in that he was present at the very beginning and could have prevented it, but it would have involved the complete destruction of an inhabited solar system which he was reasonably reluctant to do.
Interestingly, wiping out the system (and the Nietzschean armada) would have forestalled any further attempts by the Nietzscheans, as they only rebelled because they felt that the Commonwealth doesn't have the balls to do what is necessary to survive.
Used in the Community episode "Modern Warfare", in which Jeff takes a nap in his car and wakes up to find the entire campus abandoned and in ruins due to a massive paintball tournament. Probably a direct parody of 28 Days Later.
Much like the other adaptions here, both the 1981 and 2009 TV adaptions of The Day of the Triffids feature a main character escaping the mass blindness because he was in hospital with eye damage at the time.
In the 2008 re-imagining of Survivors, Al Sadiq is too busy picking up a girl at a nightclub to notice the news reports of the growing pandemic. After taking the girl home and having sex with her, Al falls asleep. In the morning Al wakes up to find 99% of the world's population has died overnight, including his latest conquest who passed away while lying next to him in bed.
The protagonists of The Last Train hibernate through an asteroid strike.
A Derren Brown special involves setting up a young man who refuses to take responsibility for his life to believe that a meteor strike is imminent and then wake up in a hospital with a fake news report notifying people about a meteor-carried Rage Plague. Basically, the guy is supposed to have slept through a Zombie Apocalypse and must now take responsibility not only for himself but a young girl and a selfish asshole (meant to evoke disgust at himself) after the Reasonable Authority Figure is deliberately made to go away. Like all of Derren's specials on this scale (although this is probably the largest), everything is constantly monitored to prevent any harm from coming to the subject (physical or mental). The goal, as usual, is not only to show off Derren's skills and knowledge of psychology but also help the subject to be a better person.
Blow, Gabriel! by Nautilus Pompilius (Russian) kicks it up a notch, to the Apocalypse Failure:
Blow, Gabriel, blow! Now it just cannot worsen.
City's so tight asleep, that Heaven itself will not rouse it.
Speaking of Gabriel... The sleeve notes to Genesis's album Trespass have this to say about the song "Stagnation":
To Thomas S. Eiselberg, a very rich man, who was wise enough to spend all his fortunes in burying himself many miles underground. As the only survivor of the human race, he inherited the whole world.
Lif and Lifthrasir in Norse Mythology are foretold to survive Ragnarok this way, leaving them ready to repopulate the world afterwards..
The participants in the Morrow Project missed World War III because they had been placed in cryogenic suspension in order to rebuild the world after its destruction. Too bad the wake-up signal was sent 150 years late.
Invoked Trope in the D20 Apocalypse setting Plague World. Long story short: aliens invade the Earth by first unleashing a deadly virus targeting humans. Humans create Rip Van Teams (Teams of soldiers placed in suspended animation) using captured alien technology. Aliens win the war. Aliens get on the Earth. The virus mutates and decimates the aliens. The last spaceship stays 300 years in orbit, not having enough fuel to leave the solar system, crashing into the Earth when it's orbit decays. The last spaceship gone, Rip Van Teams awake to reclaim the world.
BIONICLE: with a twist; Mata Nui's falling asleep plummets him into Aqua Magna, in turn causing the apocalypse, known as "The Great Cataclysm" to the inhabitants, inside his body during his unconsciousness. He does eventually wake up, but only for Teridax to steal his body.
You might say this of Gordon Freeman in Half-Life 2. After Gordon was placed in suspended animation by the G-Man at the end of the previous game, the sequel begins a couple of decades in the future, during which time the Earth had been subjugated by the Combine. The G-Man awakens Gordon and apparently strategically places him in City 17, leading the events of the game.
G-man : Rise and shine, Mister Freeman. Rise and... shine. Not that I... wish to imply you have been sleeping on the job. No one is more deserving of a rest, and all the effort in the world would have gone to waste until... well, let's just say your hour has... come again.
The protagonist in System Shock spends six months in an induced coma healing up from an operation to install a neural interface, awakening to find that SHODAN has turned Citadel Station into a chamber of mutant and cybernetic horrors. Nice Job Breaking It, Hacker. (Not really his fault, though: he was given the implant because it would keep him on ice for six months, in case Edward Diego needed him again)
Happens again to a different guy in the sequel, only this time it's a Hive Mind of mutant worms and their Body Horror hybrids that has taken over an experimental starship. The worms were created by the Big Bad from the first game. Who is also still around.
Will/Ed in Advance Wars: Dark Conflict/Days of Ruin is a variation - as soon as the meteors started raining he barricaded himself into a kitchen supply room to wait to be rescued, but by the start of the game he's been in there so long he doesn't realize how bad it really is outside.
A minor example in Bowser's Inside Story: Luigi manages to sleep through not one, but two Bowser attacks, only waking up just before Bowser inhales him.
In the game Rage, the protagonist was deliberately sealed in a vault to survive an asteroid impact.
The novel explains that he was a seasoned Marine Lieutenant, and that he'd been sealed along with the others so they'd have someone who'd protect them.
In I Miss the Sunrise, Ros (the player character) was kept in a suspension tank during the Shine, so they have no recollection of it.
One of the game scenarios in the Atari JaguarAlien vs. Predator game has the player as a Colonial Marine who was placed in 30 days' cyro-sleep as punishment for for striking a superior officer. When he wakes up, everyone else is dead as the space station is overrun with the aforementioned aliens and predators.
In "Fallout 3" DLC Mothership Zeta there are apparently thousands of people abducted and frozen from the time before the war. The most notably is Elliot, an army field medic abducted during the battle of Anchorage and was frozen then. Your other teamates break it to him that the world was nuked.
"Fallout: New Vegas has Mr. House who was awake during the apocalypse itself but knocked out saving Las Vegas from nuclear annihilation. While he was out the dot of civilization he preserved was swallowed up in the post nuclear wasteland.
In The Elder Scrolls V: Skyrim, the Dawngaurd expansion takes this Up to Eleven with the vampire, Serana. Being trapped in an underground shrine for at least two thousand years, she slept through the corruption of the Falmer, the extinction of the Dwemer, the transformations of the Chimmer and Orsimer, the Dragon War, the founding of the Cyrodiilic empire, the shattering of the Staff of Chaos, the Warp in the West, the destruction of the Heart of Lorkhan, the Oblivion Crisis, the eruption of Red Mountain, and the Great War against the Aldmeri Dominion which resulted in the banning of Talos worship. She wakes up in the middle of the Skyrim Civil War and the Dragon Crisis. Depending on your actions, she could have also slept through the Eye of Magnus almost destroying reality, the aforementioned Dragon Crisis, and the return of Miraak.
Not really an apocalypse (but a prequel to one), but Roger Wilco in Space Quest I: The Sarien Encounter sleeps through the Sarien attack on the Arcada and the slaughter of everyone aboard. The only reason the Sariens missed him is because nobody bothered to check the broom closet.
Chimera.Goat: Well... wekinda fell asleep for a bit...
Bob: Asleep??? This crap's been going on all year!
Chimera.Goat: What? (to Chimera.Lion) You and your stupid catnaps.
Only Human, Ely was in hibernation capsule through the events that brought end to the humanity. She is awakened 500 years later.
This short Creepypasta uses the trope surprisingly well and quite literally.
In the second Monster Hunter World arc in We Are Our Avatars, everyone spent the last 7 days high on Samus's super marijuana after their camp caught on fire and they woke up to the apocalypse.
The Arthur episode in response to 9/11, entitled "April 9th" focuses on everyone's post-traumatic stress after Lakewood elementary catches fire. Everyone except Buster, who slept in and arrives as the firefighters are cleaning up. As a result, the fire doesn't feel real to him, causing him to be alienated from his friends
. "It's not a story Buster! It really happened!"
In the first episode of Futurama, Fry is accidentally trapped in a stasis capsule for nearly a thousand years, and sleeps through at least two apocalypses and a period of reconstruction resulting in a far future that's a lot like the present, but with robots and spaceships.
Later, an old girlfriend convinces him to travel to the year 4000 in "The Cryonic Woman", where the world is a post-apocalyptic wasteland ruled by children. However, it turns out he's still in the early 3000's but ended up in a bad part of Los Angeles.
Apparently he indirectly caused the apocalypse, both times. Due to a time paradox.
In a "Treehouse of Horror" episode, Springfield gets hit with a nuclear missile at the exact time Homer happens to be in a bomb shelter.
Another episode featured the whole family falling asleep in church, and showing all their dreams. When they all wake up in an now empty church, they're embarrassed, but Homer says "Ah, it's not the end of the world". Then he opens the door, and finds out it is.
Avatar: The Last Airbender: Aang was frozen in an iceberg for 100 years, which is how he survived the total genocide of his people. By the time he awakens, almost everyone he knew is now dead, and he isn't even aware of the Hundred Years War going on. Later parodied in one of Aang's nightmares in "Nightmares and Daydreams".
Ozai: Wake up Aang. Wake up, sleepyhead. Rise and shine. You overslept. You missed the invasion!
Mentioned in a throwaway gag in The Rugrats Movie: Grandpa falls asleep watching the kids, which allows them to leave the house unsupervised and sets the movie's plot in motion. Deedee chews out Stu for leaving Grandpa in charge in the first place.
Didi: Stu, the man slept through Pearl Harbor!
Adventure Time has "No One Can Hear You", when Finn is knocked unconscious and wakes up to a completely empty Candy Kingdom, save for a stark-raving mad Jake.