Son-in-law?

We can not answer "your question it is not clear" The person you are referring to could be anybody bought into the/his wife's' home (for any reason). People can or may and are assuming you are meaning an inlaw and they are jumping to the conclusion it must be a son in law. However, we just do not know. It could be a sex slave, a servant, a carer, caregiver, a butler, a manservant, a housemaid, a chauffeur, a friend, (anyone you took pity on and are giving shelter), (anybody you brought home or invited home and offered shelter to from your work or possibly charity for which you work) etc forever the possibilities are Endless. It could be an illegitimate child of either the wife or even anybody who is or isn't living with the wife. I have answered the question according to what you actually wrote. "My wife's parents are very old and ill I need someone to come and live in their home to be with them" what is this person called in English so that I can find such a person" "a home help" "a caregiver" "a carer" "a volunteer" "a befriender" and other names

We don't have a polite word for these people. It would be an unusual and mostly unwelcome situation. But he is the 'son in law' and they are the 'in laws'(his mother and father in law)

A caregiver?