During the last year it was rented it to tenants that put a lot of damage in the house.

He'd accepted an offer of $120k before the other buyer pulled out.Link to Zillow ListingI know he's had quotes of $30k-$50k to put a new roof on and repair some structural damage due to neglect. 

It can be two months and security, or 3 months and damages from security.

Ive moved out and she wants to rent the property but obviously has to be repaired from the damage. 

Also, if they leave the place without damages, clean, and ready to rent (quick turnover), then I would consider returning the security deposit.

My concern is that the unit under eviction will be heavily damaged with no security deposit and insurance doesn't cover tenant damage, though a criminal act.

Then I either get better than average rents or I'll sell it.First I repair/replace things, if needed, that cause more damage (to property or life) if they fail, roof, water heater, plumbing & electrical... anything health and safety related. 

I've been reading about landlord insurance to cover liabilities and damages.

I've had dozens of pets in our units and they have done less damage than bratty kids, and you can't charge extra for Rugrats!

If that happens, it could result in damage to your property, such as a broken down door.Third, get inside the unit.