Most rabbits will chew through a plastic tablecover. Some heavy duty tarps might work - depending on the bunny.
Do you have a photo of your cage? That might help us to figure out options.
Thin plywood can have self-stick vinyl tiles put down, or a piece of rolled linoleum. It's a good idea to have a water proof flooring down like the vinyl or lino and then you can always put fleece or a pet bed in there for them.
Other than the wood pellets in their litterbox, my rabbits cages don't have any loose bedding. I'll attach a couple of photos of current and past cages so you can see some options. Sorry the photos are so big - not sure how to adjust.
The NIC cage has rolled linoleum for the floor. That may be your easiest option. I just made sure that the edges went slightly beyond the cage edges so that bunny couldn't get to the edges and start chewing.
The smaller NIC was a temporary cage, but if you look close, you can see rolled linoleum sticking out under the rug just outside the cage. So in this case, the lino serves to protect the carpet just in case. A shower curtain liner could do the same thing since the rug is on top.
The x-pen just has fleece on top of carpet (bun is fully trained).
The wooden cage has actual tile (though the walls have the vinyl stick tiles on them.
