My MIL is also in an assisted living facility, has dementia but still remembers everyone. I would hesitate to make her a quilt, especially one with pictures printed on fabric. Something like that requires special care when being washed, and that's definitely not the case in most facilities.
Also, as someone else stated, things go missing on a regular basis. I see towels, sheets, even clothes in her room that I know are not hers. I have no idea who has the nice towels we bought her, but she definitely doesn't.
If you want to make a quilt, I'd recommend a wallhanging that doesn't need to be washed. We had a picture made for my MIL with a tree in the middle, and pictures around it with all our names on. She loves the picture and often looks at it and asks about the people in it. Maybe you could do something along those lines?