Most often, cryogenic preservation, the intentional freezing of the ill or declared dead, is used simply as a plot device to introduce a fish out of water or time travel story. The method of stasis and their medical condition are waylaid to the events that happen after they are revived. It's rarely used as a central theme in fictional writing. There seems to be no mainstream movie broaching the subject by itself. That said, it does pop up in a few shows.
Star Trek The Next Generation episode "The Neutral Zone""The Neutral Zone" has the B-plot (Human centric story) of a cryopreservation ship found by the Enterprise. The humans inside were terminal at the time of their freezing, while current medical technology is able to cure all of their diseases within minutes of being revived. Then it dwells into their confrontation of mortality (their own and everyone they knew) and culture shock, having been born in a capitalistic society now faced with an egalitarian one.
Stargate SG-1 episode "Lifeboat" revolves around the complications of cryo stasis when the bodies die due to power failure, but the minds are kept alive in others.
Most notably, the CW is reported to be developing a drama centralized around a medical breakthrough in cryopreservation:
This is an interesting pairing between subject matter and a producer at the CW — the network is working on Cry, a drama about the prospect of eternal life via cryogenic preservation that comes from Paulist Productions, a Catholic media company.
Written and executive produced by Kerry Lenhart and John J. Sakmar (The Glades), Cry tells the story of a doctor who makes the astonishing medical breakthrough to bring cryogenically preserved people back to life, starting with the unfreezing of his own father — but he never expects that restoring life will have both glorious and devastating consequences.
Paulist Prods. executives were attracted to Cry because it explores the moral dilemma cryogenics poses on relationships and society.
While Cry features Cryopreservation, it still focuses on the interpersonal drama, instead of being a medical drama, ala E.R.