I don’t think that the affidavit of support (I-134) gives any rights to debt collectors. It is a document in which the sponsor promises to ensure that the visitor does not become a “public charge”. It is not a broad agreement to pay all their bills.
The real danger is that, when you told the hospital that your father had no insurance, they may have asked you to sign a paper that you’re financially responsible for him. If you did that, you’re screwed.
I am not a lawyer and this looks like a situation where you might want to consult one.
