The problem is not that the monster likes to eat our parts, but simply, as I have observed, it likes to play catch with itself. Drop a piece and watch it bounce accross the room. So what you have to do is;
A-take up the rug and put down a solid floor, something without gaps or cracks.
B-cover everwhere that you do NOT step with double sided tape.
Sounds like alot of work, but not a single piece will ever bounce again.