@Lars52 well I sure would not like to receive a message OR an email like that!
I am not a lawyer, so I don't know exactly how things go (especially since you are in another state), but this sounds not much different than old fashioned extortion.
In California, if someone sues you, you have to be served the legal paperwork, normally by a process server. There is a huge gap between being served the legal paperwork for a lawsuit and receiving an email claiming that someone is suing you.
Since the insurance this person is offering would not cover the event that already (supposedly) happened, there is no advantage in buying it right now. If the person tries to contact you again, ask them when you can expect to be served with the paperwork for the lawsuit. And ask them how they know about this lawsuit already. Are they the lawyer representing the injured party? If so, why are they contacting you to sell you insurance? Are they an insurance salesman? If so, how do they already know about this lawsuit? So many questions.
Again, I am not a lawyer, and I am in another state, but in California lawyers don't go around trying to sell insurance, and insurance salesmen don't know about lawsuits that haven't been filed yet.
And these people work with AirBnB?