If a ring system is not stable, there are only two places for it to go. The debris is either flung out to space or goes crashing down to the planet/moon (or what ever it is circling). This may be what it looks like after it goes crashing down.
Picture embedded below.
"There’s a new theory for why Saturn’s moon Iapetus looks like a walnut. The moon has a mysterious large ridge that covers more than 75 percent of the moon’s equator. Figuring out the reason for the ridge, say researchers from Washington University in St. Louis, has been a tough nut to crack. But they propose that at one time Iapetus itself had its very own moon, and the orbit of this mini-moon-around-another-moon would have decayed because of tidal interactions with Iapetus, and those forces would have torn the sub-satellite apart, forming a ring of debris around Iapetus that would eventually slam into the moon near its equator."