They will probably sue both if anyone. Hopefully there is homeowners insurance, renters insurance, or both. If not, there could be a judgment. So if there is insurance, turn it over to them. If not, then hire a lawyer to defend them and do it sooner rather than later.
This is not legal advice. You should always discuss the specifics of your issue in person with an attorney. Be aware that there are time limits on all claims that depend on the kind of claim, so do not delay in seeking an attorney.
Sign up to receive a 3-part series of useful information and advice about personal injury law.