For something like an SSL/TLS library, you could have a fuzzing mode that sets the initial randomness to a fixed value. That lets you create a pre-baked input file that can successfully establish a session, and you'd start the fuzzing from there.

You can do the same thing with session IDs or similar. In general when you're fuzzing you want to fix your random seeds (and date/time inputs etc, as well as reset any external data store modified by the program back to initial conditions) - ideally your program being fuzzed is a pure function of its input.