Prosecution for WHAT? Falling off a bar stool is not a crime, it's just stupid.
Perhaps "public intoxication" laws could be used, but in general the police only use these laws to jail loud, obnoxious drunks who are being a pain in the butt.
We don't know if the bartender was serving her, in her intoxicated state, or if she was drinking somewhere else previously.
If the former I think the bartender should be given a talking to. It's not smart to serve people who are visibly intoxicated, and illegal too in many states.
If this is frequent behaviour a rehab clinic is exactly where she belongs. Regardless of her politics I hope she and her family are successful in getting her into recovery.
You are a great deal more sympathetic and perhaps gullible than I am perpared to be here.