During an earlier stage of her Alzheimer's disease, Mom went through a lengthy phase of picking at the skin on her neck, arms, and ears. She said she did it because she liked to do it and no strategy I implemented was very effective to stop her. Common suggestions for such problems include keeping the nails trimmed very short and providing small objects to keep hands busy, but these efforts didn't help Mom. More effective were engaging videos, a walk, or other activities that removed her from the environment where the behavior was most likely to occur: her beloved chair.
Picking at the skin is dangerous because of the possibility of infection. During Mom's skin picking phase I bathed her scabs morning and evening and applied antibiotic ointment. Bandaids were useless because she would immediately pick them off.
Mom has stopped these compulsive behaviors and I'm not certain whether they may recur or if she has moved on in the development of her Alzheimer's disease to a stage when compulsive behaviors are less likely. The skin on the back of her neck bears scars but the wounds have healed.
This was a frustrating time and I had to fight anger toward Mom because it often seemed the behavior was rebellious. It was almost as though when she knew this was something that upset me, it gave her power over me, and so it became important that I projected acceptance. We got along much better when I did not act surprised or angry when Mom picked at her skin. A matter of fact dressing of the wounds along with distraction to an activity such as a snack or a video worked much better.
There are helpful articles about compulsive behaviors at the sites below: (not certain you can access the first link unless you subscribe to the Caring Right At Home Newsletter at caring.com):
Caring.com - Picks Obsessively at Skin or Small Objects
Mid to Late Stage Caregiving Packet from the Alzheimer's Association
Good article on "bad" behaviors from agingcare.com