About a few months ago I had several cats randomly fall from the sky (I don't even know) and they fell in the trees of my garden sim, there were 3-4 of them, but I noticed them stuck on some treetops while clearing prims and retrieved them. All of them were sick cats too already laying in their bed poses.
I clicked on each one and noticed they were cats I had menageried so long ago, I'm not even sure I had menageried them on that same sim. So maybe it's not impossible to retrieve cats from the menagerie? Perhaps there's other reasons as to why they don't wish to retrieve kitties from the menagerie.
I'd like to say I re-menageried or deleted the others that had fallen thinking it was some error but I don't recall what I did, I was just shocked at the whole incident and excited to keep some of these kitties I regretted menagering. I kept Pidgeon and Pidgeon's Fortune, both were menageried months before - I was so glad to see them because I had missed my Burmese Blues. I cured both of them too without issue and when I let others own these kitties to see that it wasn't just a glitch but kitties that actually came back from the menagerie somehow, it too said menagerie on the pedigree for them as it does for me:
Pidgeon's Fortune lives happily in my cattery at the moment.

She also walks around, chases butterflies, catnaps, and does everything in-world like a normal kitty would and has no issues, she eats food too and seems to have all of her "data" there despite having been menageried.
...And that's how I became known as the kitty necromancer.