You should thank your neighbor.

There is no value for a half dead tree in USA. You may hope
it would getting better, but the truth is it most likely
will not. Then you have to take it down either by yourself
or spend money to do it. I would like to get rid half the trees in my yard, but none of my neighbors would come to
take them down for me. If you really like to have a tree,
plant a tree you really like and put it a little inside your yard.