The way I've used this is saving my python repl process. Sometimes when I'm just hacking stuff out I will define things in the repl without writing out to a file. But then if you kill your process or it dies or you move to another server you lose anything that you defined. With this I can save my repl state and restart it later, move it to another box, and make pancakes.
It used to be common practice to coredump a Perl script and edit it in debug so that you could skip the initialiastion phase of a frequently run script. This was most commonly performed on CGI scripts. CryoPID would make it trivial to do this task in any language via the script itself.