Ordinarily a parent is not liable for an adult child's bills unless there is an agreement that the parent signs to co-sign on obligations or bills. This would include possibly signing documents at the hospital agreeing to be personally liable for those bills. It would be important to see any documents from the hospital that might purport to obligate the parent for those bills. It sounds like, from your account above, that you may have signed something agreeing to be liable for the bills. If that is the case, the hospital could certainly pursue you and attempt to obtain a judgment. It would be imperative to look at those documents that you may have signed to see exactly what they say.