I read this book in the 80s and am unable to think of the name. The story begins with the main character coming out of a stasis bubble. These bubbles were of different sizes and some were huge, covering cities even. At some point in time (through flashbacks) some of the bubbles even became dislodged from the Earth and floated out to space, carrying all contents with them.
This is probably Marooned in Realtime by Vernor Vinge, or just possibly one of the shorts that were incorporated into the final form of the novel. The bubbles were called "Bobbles" and were originally thought to simply insulate the inside from the outside, forever -- thus anyone caught inside a Bobble was believed dead. It wasn't until a lifetime later that the first Bobble burst and revealed the interior to have changed not at all in the intervening half century.
Once that was known, and the cause/effect of how long a Bobble would last could be controlled, they became widely used for things like shielding, long-term storage, and time/space travel (a trip to another star might take centuries -- but with Bobbles, only the time your system needs to check conditions and re-Bobble would be perceived; the trip would seem to take a second or so).
The actual novel follows a small group of people who, due to Bobbles, missed the "singularity" in which humankind vanished from the Earth.