I have a rabbit cage inside my buns' enclosure, typical plastic bottom kind. They use it as a bed and a litter, I just leave it open.
Recently, after both my buns turned up with sore hocks, I've been going on a renovation craze, improving all the flooring.
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You can give rabbits carpet, but the kind depends on your rabbits. The best kinds of carpet is that made of natural fibre: jute, sisal, or hemp. This kind of carpet is safe for rabbits to chew on, and if they eat some it's no big deal. However, most natural fibre is woven into a flat mat, which does not provide much cushion for your rabbits' feet. Any natural fibre carpet with a good depth to the weave will be quite expensive.
If you can't go for natural fibre, then you must be absolutely sure you get pile carpet, not loop. Loop carpet is made of one continuous strand, looping up into the carpet's weave. If your bunny tries to eat it, they can eat it like a spaghetti noodle, and end up with an entire length of indigestible material clogging up their digestive system, which will of course kill them.
Pile carpet is made of very short strands folded in half around the carpet base, so that the ends stick up. If your rabbit tries to eat it, they are in much less danger of choking or blocking.
Deciding if polyester or other plastic-based carpets are safe is entirely up to you and your rabbit. Some rabbits are fine with carpet--others obsessively chew on it.
Before I went and bought a ton of carpet, I gave my buns a trial carpet by taping down a piece of polar fleece. Polar fleece is very safe for animals, because if you put a hole in it, the hole will stay there and not unravel as most fabrics would. In other words, in order to eat more than a tiny piece of fluff, a rabbit would literally have to sit there and gnaw out a circle in the fleece.
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So when several months had gone by and there were only a few tiny holes in the fleece, I knew that it was probably safe to try them with a carpet.
Finally, recently I decided that the shavings in the cage were insufficient for proper flooring--they'd dig them aside and stand on hard plastic. So I went and bought some timothy grass mats from a pet store--three fit perfectly on the bottom of the cage, and stayed under the shavings. They also helped make less of a mess, because half the reason that they found it so easy to push shavings out of the cage was because of how slippery the floor was. Now they can't just shove all the shavings in front of them like a snow plow, as the grass mats do not let their paws or the shavings slide across them.
Hope this helps!