As a nurse who worked in nursing homes, I will tell you that this happens alot. And it saddens the staff that work with those residents the most. Somehow it goes to laundry and never comes back.
One home used security cameras and watched as some staff took garbage bags out. Thinking that they were just taking out trash, they had stashed the bags full of various pieces of personal items from the residents. It is better if the home uses clear trash bags so that contents are not hidden from view.
What you did with your label is what I suggest, quilt it into the quilt so it cannot be removed easily. I also fuse them on before I quilt them. So sorry this happened. If you haven't already, go to the administrator and tell them the issue. (It doesn't hurt to show that you are upset--not screaming- to show that you are not just going to be ok with the standard response. Be persistant. Ask about it everytime you show up and make it known that this was taken from your sister's room. Believe me when I say that sometimes it takes mentioning it again and again.