What your tenant did is called "Negligence" otherwise known as stupidity.

It can be a gray area, but generally if you were not negligent in upkeep (as in didn't ignore requests from tenant that there was a possible issue) you aren't liable for the tenant's belongings.

—If the premises are damaged or destroyed other than by the wrongful or negligent acts of the tenant so that the enjoyment of the premises is substantially impaired, the tenant may terminate the rental agreement and immediately vacate the premises.

But, your neighbor's policy may cover the damages if it can be proved that the tree fell due to that person's negligence." - Located here.

Of course, if it is not habitable because of landlord negligence, that's a different story.If a unit floods because the sewer main collapsed unexpectedly, the landlord most likely bears no responsibility and -- according to contract -- is not responsible for motel room bills.I have seen a landlord being forced by the city to put tenants in hotel rooms -- 1 week for adults and 2 weeks for adults with kids, because the city red-tagged several buildings.Now, what you are legally obligated to do, and what you may end up doing for good-will reasons, that's not the same.No legal advice given.

Worst case scenario is probably you lose all of your investment, and do something negligent that gets you sued for more than the asset.

I like to assume negligence instead of malice.

But the odds of a section 8 participant with negligible real income who still has good credit,  good landlord references, and no criminal history are probably fairly low.   

If it's any more than that I would request that he transfer the property to another PM to prevent any of his negligence coming down on your head. 

They'll say the landlord was negligent for letting you have it, blah blah.