I put organza bags on figs to keep off birds and bugs off, but sometimes find them still being stollen, bag and all, by squirrels who chew through the cloth. I find chewed up organza bags all around the yard. But it still helps me keep some of the figs.
I think anything that likes sweet fruit will go for figs once they get a taste. I was in Washington DC at a kayak rental place once and saw this big, mature fig tree covered in fruit. Several branches were shaking and I thought it must be birds, but when I looked closer I realized there were about a half dozen rats gorging themselves on the figs. In broad daylight! It made me think my squirrels weren’t such a big deal.