It's called 'Tonic Immobility', and it's not cool. Edited by Hayden Hoyl. read more
From what I've seen, mostly no. They usually sleep on their bellies but they do flop over on their side and stretch out when extremely happy / relaxed which may look slightly like they are sleeping on their back from the right perspective. read more
Rabbits can easily be injured if they aren't handled carefully, but laying a rabbit on his back doesn't instantly paralyze him. A rabbit can be put into a trance-like state of paralysis, however, by placing him on his back and flexing his neck. read more
Rabbits are cute and soft, but they can be more difficult to hold than other pets. Flipping your bunny onto his back is not necessarily a bad thing. However, use the proper handling techniques and take precautions so your pet does not injure himself when held this way. read more