With a verbal agreement, what rights does a landlord have?

Question Details:

I had a verbal agreement with my tenant to pay month-to-month rent; I didn't charge a security deposit because we agreed that if they broke it they would fix it. They only had a mattress, so I borrowed a bedframe from a family member. I told them to watch it and let me know if they needed pads for the frame so as to not damage the floor. The tenant suddenly moved out without giving me any notice and left his girlfriend to pay for everything. There are damages to my floor and wall which they refuse to pay because it was my frame and there was no signed lease. Is there anything that I can do?

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