It would have nothing to do with you. Obviously, You don’t want to have that dog owner as a tenant though.
You cannot party to the suit because you were not the owner of the property at the time the incident occurred. Since you have knowledge of the incident you may have a subpoena issued but you definitely would not be a party to the suit.
There was a podcast recently that discussed buying properties with legal issues. Might have been 279 or 280, can't remember. Anyway, there is legal documentation you can get signed that essentially releases you from any and all legal issues w/ existing owner. Maybe someone here can narrow down the podcast and you could look into that.
I believe that the issue is more to do with prospective damages against the current property owner. If the suit has been reduced to damages and those damages are not paid, there is a potential that the claimant might attempt to attach a lien on the dog owner's property to compensate for the non-payment. The damages collection process is a world unto itself in the legal community, and that process is well beyond the scope of a short answer here.
Presumably, any property liens would show up on the title and the title insurer would either exempt the lien or insure over it. This is where you want a good property lawyer who can verify that you're getting a clean title.