She is rich, rude and cranky. She was Eleanor Shellstrop's roommate when Eleanor was alive. She was victim to Eleanor and her other roommate, Brittany, in the "Dress bitch" business after an argument and law suit with the dry cleaners after Eleanor wore her new dress without permission and ripped it.
In the second timeline when Eleanor is trying to be good, Eleanor admits that she and Brittany were behind the "Dress bitch" shirts. Madison storms off in rage and moves out.