ah, so that is the same tree, from which a part fell recently! I thought this was a second tree that has problems! (Like you needed more problems.) Perhaps, then, the part of the tree that looks like it has no bark is where the other half split from, when it fell to the ground!

I do hope the neighbor (or his landlord) will split the cost with you. Having an entire tree removed can be expensive. GOOD LUCK with it!