Tree question

My father is concerned that several trees that straddle his property line (but mostly belong to his neighbour) are getting old and need to be removed. His main concern is that if something happens and a tree falls on his house is that insurance won’t cover the cost of repairs because he ‘never talked to his neighbour’ about his concerns over the trees. I don’t know, this doesn’t seem like something the insurance company would ask, but I’m hoping to get some insight from this sub Reddit. TIA!