There is a time-travelling debugger that forks the process at each statement, allowing you to go back to a previous statement and continue from that point.
Why not? (Experimental) versioned file systems exist.
But I think the idea has been around forever.
There's more to checkpoints than just fork(), though; for example, when two processes are sharing memory, checkpointing the process group fork()s both processes and then must explicitly duplicate the shared memory region, otherwise the checkpoint would share memory with the original, which would be disastrous. Unfortunately this means we don't get COW behaviour for shared memory regions; unfortunately the Linux/POSIX APIs are a bit deficient here.
It has another mode where you can record and rewind execution traces, which sounds more like the description, but I'm almost certain that doesn't use fork. https://sourceware.org/gdb/onlinedocs/gdb/Process-Record-and...