Hi there. My bun has lost her nail before (Scared me to death) and we just cleaned it up and watched it, making sure everything was clean. She had a vet appointment about a week later for something else and when the vet techs (yes it took 2 to hold her and clip them) saw it they really didn’t even mention it. But there was a tiny stub of nail left. If there is still a nail stub I *Personally* would just keep a close eye on it and keep it clean. If there is nothing there I might consider taking a vet trip.
But I would definitely secure the room better. I understand it can be difficult (I currently have 2 adult dogs and we just rescued 2 puppies and my brother also has his dog staying here so 5 dogs) but a door that can be latched completely shut, an eye hook lock thing and a baby gate are all good measures to make sure there is 0 chance of any of the pets getting in there if you don’t want them too.
Good luck! 