Congrats on the new job.Some things to keep in mind is to have systems in place : maintenance,bookkeeping,management, filling vacancies etc.Know your SWOT  (Strengths, Weaknesses, Opportunities, and Threats)The city requires a property manager if the owner lives more than 20 miles from the property.

I know of a property that was bought, the seller claimed there were valid leases, but the day after closing he disappeared and disconnected his cell phone number.

What happens if "the couple" disappear and leave you with a bunch of strangers?

Or you can install a split A/C system that will cool better and remove the threat of theft.

Pay the ground rent off , so it disappears .  

What would happen to a property manager if February rent all disappeared or was frozen?

He is getting a 1099 from the government on this money and will have to pay tax on it (unless property is held in an IRA).You should be entitled to receive the 3 months while you owned the property.I would contact him and threated to report him to the government for fraud on receiving the 3 months of rent on a property he no longer owned. 

The punitive damages part of his threat beyond the deposit itself makes me nervous as well (not sure I have reason to be), but that is the point of him including that.What advice do you all have?

The last mailing I did out of state, I received a voicemail with all kind of threats and uncensored language. 

she disappeared in the night after I had to evict her for non payment and so did my refrigerator.