This is a rare occurrence, but has happened a fair number of times with Airbnb guests. For some reason, most of these squatter situations have been in California. There was one in Palm Springs, one in San Francisco (Nancy referenced that one), one in Watsonville, one in San Diego, and also one in Texas, all within the last 2 years. Probably more than those, but those are the ones I know about.
Generally if a guest squats and refuses to leave in states/regions with tenant protection laws, you have to file a lawsuit (unlawful detainer suit) to get them out of your home, and this can take time. HEre is a story where it took one man 274 days to get what seemed to have been a practiced scammer out of his home: Squatter horror story
The fact that it can take so much work, and time and money to get someone out of your home, who is essentially scamming the system, makes me feel very strongly that "the system" needs to be fixed to prevent this. These are not people who had signed a lease to live in the property in an ongoing way, and so they had no right to expect it to be their "home." They were there for a very clear and definite short period of time, and I see no reason why the law would make it so difficult to get someone out in such a case. One should not have to go to court to get such a person out, but unfortunately, that is the way the system works now.
My hope is that AIrbnb would be able to cover the costs of any host who has to deal with this sort of problem. Particularly since these problems occur rarely, I would think Airbnb could cover the costs in each case, through either the host insurance or host guarantee.