This happens even in the best of nursing homes. I worked in one where after looking through security camera video they finally found that an aide went out the back door with a garbage sack, but never put the garbage in the dumpster. That sack went to her car! That is how she took a quilt out of the home. Of course, many could never be traced that far.
It is ok and suggested to make quilts for nursing home residents, just that don't make them cute or terribly personal. I've even heard the uglier the better. And give them to the home, and not a specific person. that way they get a quilt to warm up with, but one that is least likely to walk out the door.