Suspended Animation

Wakko: I hate being in suspended animation.
Yakko: I thought it was just cheap animation.
Animaniacs, "Our Last Space Cartoon, We Promise"

There is a fairly good chance you came here looking for something about people moving into the future or coming from the long-ago past by taking a really long nap. We call that a Human Popsicle.

On the off chance that you had more interest in the idea of people who seem in the story to be inanimate, we have Faux Death.

Neither of these meanings is to be confused with an animated series that has been canceled and then Un-Canceled.

Oh, there's also the Infocom game, Suspended.