Blanket with fuzz that can be picked off?

This seems really weird but does anyone have any blanket recommendations for blankets that have pickable fuzz? I barely know how to explain it...

My toddler pulls out and eats her hair when she's stressed out or bored. We have been trying everything. One thing that I thought might work was picking fuzz. When I was little I had this blanket that basically was made to put on your bed between your sheet and your comforter to keep warm, and I used to pick at it and pull the fibers out and make so much fuzz. It was incredibly soothing. I can't help but wonder if she would find this soothing as well, only I don't know if they make this kind of blanket anymore (or what it's called). I have yet to find any blanket with little weaved fibers that can be picked off into fuzz. (Wool? I honestly have no clue. I feel like we used to get them in the home section of department stores.) My hope is to find a blanket that she can pick fuzz off of and hopefully that will discourage her or distract her from pulling out her hair.

I know this is weird, but I appreciate any help! Thank you!