In many places the business facilitated by Airbnb is illegal. New York state, Chicago, and many other places have strict hotel laws that forbid these kinds of informal apartment rentals. It is extremely unlikely that any one can buy an insurance policy to cover an illegal transaction.

If you read the Airbnb TOS you'll see that they are well aware of this and are just hoping that naive customers don't read the whole thing.

I expect the original poster's losses will not be covered by home owner's insurance.

http://www.nysenate.gov/press-release/illegal-hotels-bill-pa...