Lawyer up. Seriously. In any way possible.
Document all phone calls. Get name of caller, the name of the collections agency, the address & phone number of the collections agency, time and date of call.
Collections agencies can only collect on a bill when you have been billed and the bill is indisputably yours and all of it, every last line-item on it, is also yours. Hospitals need to send you an itemized bill that notes every last item they are billing you for, down to the name and number of medications received. They cannot surprise you, send bills to collections that have not been legitimately billed in other ways, send you bills that are not yours, or bill you for services you never received.
Make no mistake, they are doing this to your mom because they honestly believe she will NOT get a lawyer to fight back, or cannot afford a lawyer to fight back. Second the recommendation to go to legal aid if possible. If the state doesn't sponsor such a thing, sometimes law schools do.
Also, write a nice letter (paper, not email) to the state Attorney General. CC it, certified mail, to the collections agency and the hospital administrators. Write another letter to the hospital administrators, CC'ed to the state attorney general and collections agency, explaining that these bills are for treatment of her ex-husband's injuries, NOT HERS, and if they wish to send a bill they can send it to (ex-husband, 1234 Main Street, wherever USA). These letters will be more effective coming from a lawyer than from her personally, but do whatever you can. Do not negotiate on the phone; if you must, for whatever reason, negotiate by phone, send a hard copy letter to the hospital and collections agency reviewing all the points discussed in the phone call. Collections agencies have a habit of claiming phone calls never happened and they never said that, type of thing, so if you have a hard copy letter documenting who you talked to and what was said, that's better proof that the phone call happened.
Do not think for one instant that these people are bargaining in good faith, or are nice people who would not want to put an old lady out on the street. They are nasty, nasty creatures, and everything I can say about them is inappropriate for a family forum.
I had to deal with these buggers when DH was injured at work and the claim naturally went to Workman's Comp--his employer did not dispute it and admitted it was their fault for inadequate safety guards. At the time WC had just been privatized by the state. The double-billing, triple-billing (i.e. billing us after the claim had already been paid by WC, to see if they could get twice as much money), the lost records that magically reappeared, the previous WC accountant who got fired, the next WC accountant who also got fired, the multiple billing, the collections agency, it was all insane. The only thing that stopped it all was a letter from a lawyer explaining that the penalties for double-billing (AKA mail fraud) were severe and would be pursued working with the state Attorney General to the fullest extent of the law.
