My Mom Has Super Vision

Do people with dementia have supervision? My mom can see a lint on the floor from across the room and try to pick it up. The problem is my mom has a history of falling down and hurting herself. I've tried to stop her cleaning activities by deverting her attentions to a family photo album or by bringing out her favorite board game or maybe her favorite movie. It doesn't work. She gets so focused on cleaning the carpet in the living room or in the bedroom that her asthma perks up. YES, I vaccum the carpet three times a week. Do you have any suggestions?