Oh dear, so the council supplied the carers, the council sent in the debt collectors and the council appointed him a social worker, who is now going to talk to the debt collectors for you!!! Is social worker also going to convince brother in law that this debt has to be paid? Because that's the stumbling block. As his PoA, I think you will have to arrange payments. If carers are still visiting and he is not paying, then there will be more to deal with. Then again maybe the social worker has a magic wand and will make all this disappear for you. Can understand why you feel in such a spin and worried the debt agency will chase you, highly unlikely and if they do, you will have to act and do whatever is necessary as brother in law's PoA. A p.s to this, debt agencies are not bad people in my experience, yes I have experience of dealing with a bailiff.
Social worker can't stop him spending a bit of holiday time with you, you are right not to mention the 'letter'.
Think with all of this going on you are now a full time carer for someone with some form of Dementia where confusion and worry rules.