State law says you have to let the unit sit for 60 days before you can clear it out if no one comes to claim the tenant's possessions.  

This happens when one spouse divests the other party’s interest in the property.Adverse possession.

If the tenant still has possession of the property, an eviction lawsuit must be filed by the landlord.

Nevertheless, I would inquire and ensure that the home is being sold with the typical new construction Statutory Warranties, and I would want to ensure that the warranty start date would be the date you take possession.

You got title of the property but they got physical possession if they're in the property.

Essentially, the criminal act of the third party was against you (more so than the tenant), because payment had been delivered to you and thus was "in your possession". 

So do they pay the entire price of the house if you lose it to adverse possession?

Nothing wrong with putting in the sweat equity, it will make you a better investor and appreciate those that possess skills you do not have.

You may be able legally acquire that strip of land under a theory of a legal doctrine called Adverse Possession.

Is this the typical renter's insurance which protects the renter's possessions or something else?