You could also remove any locks between the basement and main house or the downstairs bedroom if they exist to discourage this behavior.  

Give you the wherewithal to pursue and achieve your long-term goalsMany investors start off "too hot", and they either overdevelop their first property or they spend their money too fast: either of these behaviors will stop you dead in your tracks, and you probably won't even be able to achieve your short-term goals - and you certainly won't have the resources to pursue your long-term goals.

Do not reward this defIant behavior and offer cash for keys , that is a hail Mary last resort . iN the sprirIt of tryIng to save money In an evIctIon , I’d make one last phone call to the tenant and explain that you are going to march down to the magistrates office and throw them out unless the animal is gone by the following day .

I'm not usually surprised by people's poor behavior but this one hurt a bit.

It's a fairly simple system to figure out, so there are investors and businesses (Mostly flippers) focus on it as a primary deal source, building a system to study properties in advance of the sale and having top bids ready to roll.There is also a fair amount of, let's call it, less than ethical behavior going on.

This is bad for the public and bad for realtors.From a game theory perspective we need to disincentive this behavior somehow or do a better job rewarding good behavior in more sophisticated agents who are competently taking on the role of adviser to their clients, beyond the cycle of market corrections over time. 

Any lender looking at such behavior would question your ability to stick it out with a project, and probably be reluctant to loan you money for your real estate.

I posted an eviction notice as a lease violation, as we do not condone violent and illegal behavior in our properties.

That s/he grossly mislead you or lied to you about a fact or facts to induce you into closing.As others have also stated, ARV is a subjective opinion and as such it may be impossible to prove a fraudulent behavior. 

The primary risk is that of human behavior: Did someone intentionally vandalize the property?