In the novel, it's implied that one of the ways for civilizations to escape early extinction is for them to become organized into Lines, where each line consists of a thousand or so shatterlings.
These shatterlings are basically just clones who are dispersed to various far-away parts of the galaxy. By the time the first shatterlings were created, there wasn't any technology that could grant humans physical immortality. So, how can shatterlings survive for millions of years?
(Note that in the novel, shatterlings were supposed to live indefinitely from the very beginning.)