An interesting one I've always thought needed more proverbial lines drawn: Neighbor has giant tree that is leaning in your house's direction. The next ice storm could send that baby in to the dirt (the dirt below your house). Neighbor doesn't care. What do?
Lol
I have dealt with this dozens of times over the years in business.
The neighbor has to be made aware of the danger, or the danger needs to be pointed out to them with professional assessment to be found liable in some cases.
If after a friendly casual conversation re: the tree goes nowhere...
What we did, was first write a letter pointing out the issue, and suggesting an arborist assess the tree. If no response, a second letter after offering to have an arborist assess, and write a report.
If no response, suggest having the arborist assess at expense of you, not them.
If no response, have arborist assess (if possible) from your property, not always possible, but in some cases of disease/decline this can be done.
If it can be done from your property, send arborist report to offending tree owner.
They are now informed of a hazard, and should the tree fall and damage your fence, house garden etc., you will have a good case to recover damages.
They can also solicit a different arborist, who may agree or not with your arborist report.
Arborist wars...
Seen this, it is an actual thing.
Generally, the hazardous tree owner needs to be made aware with a professional assessment that his tree poses a hazard to neighboring properties or structures, and once notified and no action taken (negligence), will be found liable for damages in most cases.
ISA Certified Arborist is who to use, not a tree guy, certified mail is how to send, not regular.