One of my favourite roguelikes, ToME (now sadly transformed into something overly complicated, which seems the fate of all roguelikes in the end, and even more sadly shorn of its Tolkienism), used to have that kind of feature. In it, you could begin in the normal way as an adventurer in Bree about to explore Middle-Earth. Or you could begin as a "lost soul" in the Halls of Mandos - a spirit trying to make his way back to the real world again. This was a considerable challenge, because you began in the deepest part of the Halls of Mandos, home to the most powerful monsters in the game. Most characters starting as "lost souls" last about 2 minutes before being squished by some ancient wyrm of power or colour out of space. (Yes, ToME gleefully mixed Tolkien, Zelazny and Lovecraft, because fuck you, that's why.)
I imagine a D&D variant of this revolving around the Abyss, where the Abyss is some vast megadungeon which is at least in part procedurally generated - between sessions by the DM, most likely. The PCs have for some reason ended up on, say, the 3654th layer. Maybe they are dead souls of Chaotic Evil types; maybe they were kidnapped by Demons; maybe the Celestial Bureaucracy just made a clerical error. Whatever the reason, they're somewhere very dangerous and they need to get out.
Another idea: the PCs begin having accidentally wandered into the dream-space of an eternally slumbering crocodilian demigod and have to find some way back to the world of the waking - while surviving the contents of a crocodile's dreams.
A third: the PCs are victims of the Lady of Pain, who has whimsically spirited them off to one of her mazes. What else is there? Other prisoners. Billions of them, amassed over the many eons the Lady has ruled in the city. All eternally doomed to wandering a world of corridors and rooms that is literally endless.
I would like to call this method of play "The Dungeon Escape" and raise it at the next annual meeting of the OSR.