Not one of her 3 sons has a couch that mom can sleep on?
Maybe one is in prison, one is homeless, and one is far away living in a mobile home without a phone?
Also there is the possibility that one of the sons is successful and has a happy home with a wife and kid(s) and thaT letting Mom stay may cause a lot of problems.
something I do not see mentioned as a possibility in these situations is that unfortunately the family member needing help may not be too easy to live with. Especially if Mom wants the other bum kids to move in with her. Or if she is an alcoholic Bipolar Manic depressive personality or some other type that gets out of control from time to time.
Of course, the three sons could all be bums without a place of their own and Mom spent all of her money trying to help them, and is now going to be broke and homeless herself. I think that's pretty likely.
It is kind of sad to think that she raised three sons and not one can help her in her time of need.