It is not criminal yet to not show up in a civil case.
You can send a fee request, but mostly you do that to show airbnb you tried and they'll maybe compensate you if they agree.
If you intentionally trash the place at a few thousand dollars level then year - nobody will probably bother other than banning you from AirBnB for life. One time we sort of trashed AirBnB (my 2 year old got hold of pen and draw on the wall and couch while we were not looking) and the only consequence was paying 400 or so in fine (max liability on listing) and stern letter from AirBnB that they may ban us if it happens again.
tl;dr mostly nothing if they don't value their airbnb account.
"A person is guilty of criminal mischief in the second degree when with intent to damage property of another person, and having no right to do so nor any reasonable ground to believe that he has such right, he damages property of another person in an amount exceeding one thousand five hundred dollars.
Criminal mischief in the second degree is a class D felony."
https://www.nysenate.gov/legislation/laws/PEN/145.10
Class D non-violent felonies are worth up to seven years in prison, likely varying widely depending on the circumstances.
I guess most states probably have similar statutes on the books. Whether you could get a prosecutor to charge it probably depends on the exact circumstances. I reckon you could find cases of people being charged on much less than $1M in intentional damage, though.
Also, yea, you can commit minor crimes that don't rise to the level of extradition then skip town. That's always been the case. So? Who is going to go to the U.S., trash an AirBNB, risk getting charged with a crime and potentially banned for life from coming back? The people who trash AirBNBs are not the same people who can travel internationally, by and large.
https://en.wikipedia.org/wiki/2014_California_Proposition_47