Pocketbook Protection from tenant damage property

[Ellen Mitchell]

Is there any type of insurance available that covers tenant damage to a property? 

I recently had a tenant move, she created extensive damage to the property (about $40k in repairs so far). I know I can sue her for $5k, and will likely never see it. Yes, I will screen better, and I wanted to know if there was insurance that could help protect my pocketbook in the future.