I do appreciate the concerns of the OP and would, indeed, recommend some gentle investigation via the officers of the vulnerability group. I would also feel quite strongly that I should be the person who attended hospital visits with my elderly parent. However, I would also recognise the autonomy of a parent who still has his/her wits about him/her. Tricky situation.
However, I was someone who cooked meals and spent time chatting and doing little bits of housework with an elderly neighbour dying of pancreatic cancer. The dear lady wanted to give me some of her "precious" things – jewellery, ornaments and so on – but never money – presumably to say thank you. Fortunately, I already knew her 40 something son, more from both of us exercising our dogs in the same park than anything else, and he was simply grateful for my input, as, apparently, all she felt she could eat were the easily digestible meals that I carefully prepared for her. I told him about her wanting to give me, or my daughter, gifts and explained that I didn't want to take her things but I also didn't want to offend her by refusal. We agreed a plan whereby I would accept earrings, necklaces, vases, statues, whatever with huge gratitude and then return them quietly to him. That way, we were all happy and we all did the right thing.