Is it the responsibility of a male relative to take care of a single female after her divorce? If so, which relative does this responsibility fall on?
Bismihi ta'ala
No, it is not the shar'i responsibility of a male relative to take care of a single female relative after she gets divorced.
If the relatives wish to do this out of good will, and for the sake of God, then that is a good thing and they will be rewarded for it. Of course, in the case of a woman getting divorced and her not having any immediate family, it is important that her kin support and take care of her and not leave her alone.
With prayers for your success.