Can a SAR worker be held responsible if something happens to the search victim?
If you mean responsible in the legal sense, probably not. You are not personally liable unless you are extraordinarily negligent (i.e., you did something that made the patient worse, even though you should have known better). As a practical matter, it is almost unheard-of for volunteer SAR teams and SAR members to be sued, and even rarer for them to lose in court.