Rabbits, rats or racoons most likely, but you don't mention where you live, so hard to know. Squirrels aren't so interested in green stuff. They'll eat your fruit for sure, but racoons are just a bull in a china closet, and break everything, and rabbits will eat everything. If you're seeing major stem breakage, it is most likely racoons or deer. I would consider putting some fencing around your figs, and certainly a motion camera to try to catch the culprit, or a Hav-A-Heart live trap, and try to trap the critter for ID purposes (and a hasty dispatching). And Gina, if it is fruit in trees, it will be ground squirrels and roof rats. Our bane. Get ready to buy a bunch of bait traps. The only way to keep both pests under control are poison bait traps. Snap traps can't keep up with our rat/squirrel population here.