Foxes and Sloths weren't meant to be domestic, so i doubt that would happen. But having pets in Glitch i dont see why not. However it might work best to have it to be an odd or imaginary animal than say, cats or dogs.
Since i mentioned odd, i decided to list some. http://en.wikipedia.org/wiki/Chevrotain
I may add more, but 1. i'm having trouble getting pictures...stuck referencing Wikipedia...and..
2. i cant get the link thing to work...so for now thats all im adding:)
I have been living in apartment after apartment building and every time the rules say no cats allowed. It's been years since i've owned a cat for real, how about a glitchen cat? Make him look however you want, cat in the hat, fat cat, or felix the cat, whatever. I love cats.
This would be asking to start a dog versus cat war which is bad enough IRL - don't need it in Ur too. Another, completely inappropriate, animal would be a fun pet. A wombat or a zebra maybe?
ETA: I just read the wiki page about the chevrotain - that would be a great Ur pet.
I dont see why it couldn't be turned into some kind of permit of thing to say you wanted to house a Tiger that eventually got larger you would have to obtain your special permit via quests and what not!
How about a parrot? It could talk. And would be smarter (and prettier) than The Rock. Possibly fly along with you or ride on your shoulder.
(+1 for a cat really)