Is it permissible for his wife to take care of a non-mahram man who is paralysed?
He is paralysed and cannot take care of himself. This means that the wife will be changing his diapers and clothes, and looking after him in all ways, because his wife is also elderly and sick, and she cannot look after him, and all his relatives are also elderly.
Praise be to Allah.
If this old man does not have anyone such as a wife, sons or daughters who can take care of him, and there are no men who can take care of these matters, even in return for payment if he or whoever is looking after him can afford it, then there is nothing wrong with a non-mahram woman taking care of him, so long as she tries to avoid looking at or touching the private part. If that must be done, then it should be done using a barrier, such as gloves and the like.
If she does these things hoping for and seeking reward with Allah, acknowledging her husband’s rights, and helping one who is sick and paralysed, then she will be rewarded, in sha Allah.
And Allah knows best.