No it probably won’t if it’s determined a storm blew it down unless the OP had prior knowledge that the tree had termite damage and should have been removed. It’s considered an Act of God and the owner of the fence will most likely be responsible for fixing/replacing.
I own the t-shirt…had a similar situation with a neighbor when straight line winds blew down four sections of four board…snapped the posts right off at the ground and my horses decided to check out his yard and turf it. I had all the sympathy in the world, intended to help pay for the seed, etc to repair once the weather warmed up, another neighbor offered his tractor to smooth out the divots. But no, the neighbor decided to try to rip off the insurance company and found a landscape guy to quote over $4K. My insurance company told him Act of God, go file with your own insurance.
He tried to claim the horses knocked the fence down, but since in fell into my property, the claims adjuster found that idea to be pretty hilarious.
A couple of years later, I was getting a quote from another landscaper and he told me that said neighbor demanded a quote in excess of $4K. He had quoted about $700. He refused to lie.
