An example of a cryogenic chamber.
Project Persephone was dedicated to cryogenics. In the late 20th century, many people of important stature - doctors, scientists, politicians - with incurable diseases or severe injuries were cryogenically preserved in the hope that, one day, the technology would exist to cure them. They could then be revived and carry on their work. Unfortunately, the holocaust ended all that, and the people ended up remaining in stasis indefinitely. Over the years, many pods failed or were destroyed by nukes or earthquakes, but others survived. The companions have found several cryocenters, but very few of those they tried to revive actually survived the process: Rick Ginsberg and Mildred are the most noteworthy.
There were only a few known cryocenters: California, Texas (destroyed by earthquakes), and Minnesota (the Shelley Cryonic Institute). The Crichton Institute was dedicated to cryonics research and had an entire wing devoted to it, but it is unclear whether or not any people were frozen or stored there.
Note: This project is not actually named in the books, though it is noted as being "one of the many peripheral projects linked to the Totality Concept" (Ice and Fire).