Mine play with the dog's rope (it's a medium size one). Every morning, it is a ritual, it is outside the bedroom door. They (I say they because I don't know which one it is) carries it up 16 stairs and leave it outside the door.

We have never witnessed actually playing with it (even by the dog), but the rope has made an appearance in every room.
I know it's not the dog playing with it because she doesn't really like toys...at four she is just starting to acknowledge that they exist (and she plays with the cat toys).