He already did. It's clear in the plain wording of the verse.
We have some responsibility to our relatives, whether or not they live with us.
Now, regarding the details:
You are being too defensive about this
@NBTX11, and this is obviously due to bad experiences you have had, so I understand why you find this upsetting. But your emotions are getting in the way of considering the matter clearly. Because you are trying to defend yourself from being bled dry by deadbeat relatives, you are looking at it legalistically, in order to find a way to argue that you don't need to do it. You are therefore missing the heart of the matter, which is actually love rather than legalism.
That depends entirely on what needs he has and how God is intending to provide those. If you are the closest person to him who is able to provide the need that he has, and God clearly intends for you to do so, then you do have a responsibility to help him. On the other hand, if you hardly know him and there are a hundred other relatives and neighbours of his who are far better placed to help him, you have no responsibility to him whatsoever. It's not a matter of black-and-white legalism around how close a relative you have responsibilities for.
Consider this wording later in 1 Timothy 5:
"If any man or woman that believeth have widows, let them relieve them, and let not the church be charged; that it may relieve them that are widows indeed."
How close does a widow need to be related to you for you to have a responsibility for them? We are not told. It doesn't say "take care of your mother or aunt if they are widows". It just says if you "have" a widow you must provide for them. Whether she is your responsibility comes down to practicalities - are you the closest person in a position to provide for her? Then she's your responsibility.
So you have no responsibility for your wife's parents if they don't need your help, and if they do need your help then you do have a responsibility for them.