Some Sleepers survive differently then others.
Sleepers are people who for one reason or another, have been displaced from time or even space. The prime example of this trope is Rip Van Winkle: a man from before the American Revolutionary War, who wakes-up from a 20-year slumber, only to find the world has changed.
This is a good method for new players to explore the alien environment of a fantastic post-apocalypse setting, with the mind-set of a modern person. A good example of this is Buck Rogers of the 25th Century, or Jefferson Turck form Beyond Thirty. When used on an alien or fantasy world, you get someone like John Carter of Mars, Den of Neverwhere, or the kids from the Dungeons & Dragons cartoon.
Beyond a device to introduce new players, this could be a viable character option for a game toying with comedy, character exploration, social cometary, or something just as unique. These characters need not be of our own time, as you could play a thawed-out Cavemen from the Ice-Age, an ancient Techno-sorcerer from a long forgotten age of unearthly wonders, a Barbarian from the Hyborian Age, an ancient Greek Hero, a western Cowboy, a 1920-30's pulp-figure (Mobsters, G-men, NAZI), or even a high-tech space marine form before the holocaust - anything is possible! The main advantage of a fairly modern person, is that they could have a better grasp of technology, but this can be overshadowed by a the inability to adapt to there strange new world. On the other hand, a character from an ignorant and superstitious era would easily act out fear and dread when confronted with advanced technology.
The easiest way to deliver a whole race of Sleepers is with an isolated community that maintained old ideals and knowledge, and has not fallen into complete decadence.