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.