I would make the management and the nurses aware that her quilt is missing and should be found and put back. Then I would never let them launder it! I'd make sure I took it home myself and did it. Its probably there somewhere, so take a picture of it with you (if you have one) and post a sign where everyone can see it.
All the best. If you can't find it, make another. In fact, make several for all the residents, then they don't have to borrow each others.