How can you get a lawsuit from a renter after they have sold the house?

Real messy law suit went on for years.

It only takes one disgruntled potential tenant to create a nasty lawsuit.

The roofing company submits a claim with the insurance company, and then threatens a lawsuit if the company challenges the overpriced roof costs submitted.

For example, lawsuits, mining rights that were sold (not a problem in Tulum), etc.

You're potentially relying on the same 3rd party outside the regs to not get divorced, file bankruptcy, lose a lawsuit, get addicted to meth (OK I'm reaching now but you get it) .

Life is too short for all of this lawsuit nonsense.

Many lawsuits are just shakedowns designed to intimidate deep pockets defendants into paying to make the case go away. 

So, the removal of occupants (former owners) will not be by eviction, but by a different type of lawsuit called an "ejectment" - eviction is handled by district justices, whereas ejectment is in a higher level of court (common pleas).

Most likely the state where the property is located is where lawsuits would be brought if they are something for personal injury like a trip and fall or something of that nature because the “cause of action” arose in that state.