I am aware of two situations where the problem was with the elderly people themselves, who were very resistant to having carers come in; and kept saying that their friends, neighbours etc were always ‘very happy to help’.
Their children could see very clearly that the demands being made on other people were unrealistic and unfair, but in one case, the older person actually refused to let carers into the house, when the children did arrange visits. Both individuals had an unrealistic sense of how well they were able to cope independently, and the children did not live nearby.
It would actually have helped the children if the friends and neighbours had been firm, and clear and said consistently they were not able to help. I can imagine how hard it would be, and of course none of us would see someone struggling in a real emergency, but it is the only way.