Fuzz is telling you to get ready to replace the string. Fraying is telling you it's long past time to replace. Broken strands are telling you you've been lucky so far, but quit messing around and get it done or it's gonna hurt you.

I figure a used bow is going to cost about a hundred bucks more than I pay for it. I immediately replace the string and cables on any used bow I get. That way I KNOW how many shots the rigging has on it, and how it's been stored and maintained. While the bow is pressed to replace the rigging, I also clean and inspect the axles and cam bushings/bearings, replace them if needed and give the bow a proper lube job.