Length contraction is an effect that literally makes things shorter in the direction of motion. Well, one of the things that relativity doesn’t change is whether or not an “event” actually happens. If the paper in a hoop is torn out, then you’ve got an event that everyone will agree on. If you’re in the reference frame of the green hoop (from your point of view the green hoop is sitting still), then the purple hoop will be smaller and will pass through. The green hoop’s paper will burst, and the purple’s will stay intact.