I've been fighting a losing battle with rats here for quite some time.
I might try wrapping the bottom of the trunk in hardware cloth, and then try fashioning some kind of metal bell-shaped barrier right above it (like what people use to keep squirrels from climbing the bird feeder pole). I'm putting hardware cloth barriers all through the dirt floor of my chicken coop.
Meanwhile, I've resorted to poison outside. I want to make sure other animals won't access it, so I had to put it in a cage that only rodents can access, and it was never touched. Then I tried putting blocks of poison in the rat tunnels, and they still ignored it.
This winter, I had a rat tunnel through the snow bank that led to my chicken fence, which was a perfect inaccessible-to-other-animals place to put poison. I chopped the poison blocks into fine pieces and mixed it with peanut butter, and then molded the concoction around a stick, like a corn dog. I was able to slide the corn dog through the fence and into the tunnel, and it disappeared over night. I think they've gone through 4 corn dogs so far, and I still have rats, but I'm hopeful that it might help.
Good luck with your poor fig tree!