I've been lucky over the last ten years, not to have any major damage to any of my properties! (knock on wood...)
I just posted on another thread that the secret to my process has been creating connection with my guests prior to their arrival and during their stay.
Having a phone conversation with them after they book, then again before they arrive has made a major difference in how guests treat my properties. I also talk to them while they are in house. The phone calls are in addition to all of the other communication pieces, like pre-arrival emails, etc.
Basically, establishing a connection with the guest has had a huge impact!
However, not everyone is going to conduct themselves as respectable human beings! I wouldn't wait on Airbnb to resolve any problem like this. You have to deal with the guest directly. That may include a small claims filing.