Obvious structure damages that was tied to other damage that was hidden.

I could see this going almost like a Usury type deal with treble damages and everything paid into the loan is credited as principal times 3....

To top it off their tenant left my house absolutely filthy with over 7k worth of damages(Photos in link below).

How do you handle damages?

There's no overlap in coverage, but the renter's policy is protective of them coming after you or your insurance for possible damages. 

Dont mind to give it back. but what if property is damaged?

Those areas are more prone to flooding and road damage from storms and hurricanes.

Do you file lawsuits to recover damages, or do you just let the tenants get away with it?

On the flip side, students can sometimes cause more damage than your average renter, so make sure you're asking for a deposit that will cover you if they destroy the place.

Ex: A house with a 15 year old roof sustains enough storm damage requiring it to be replaced and the roof damage is estimated at $20,000 and assume a $1000 Policy deductible.Replacement Cost - will pay out $20k for the roof minus deductible.