Those Mylar birthday balloons will do just that, if you leave them in the corner of a room long enough. Eventually, enough gas will leak out that they'll settle toward the floor -- until the string touches. The weight of the string is just enough to bear them down, but once the string touches the floor, the balloon will stop settling and float about the house, sometimes for weeks. We had such a balloon a few years ago. We were likely to find it anywhere in our three story house. It would go up and down stairs, bump into the back of your head while watching TV, etc. We joked that it was haunted. As more helium leaked out, it settled lower on the string until finally it dragged on the floor and we got rid of it (and perhaps the spirit that drove it).
Dangerous Bill