My idea is this.
When a user is banned, no matter how long the ban is, all their pets are moved onto their profile (and/or their shop/showroom is deleted to make this easier to accomplish).
If the ban is permanent, well, problem solved. If the ban is 3 days or something, some pets may die depending on how hungry they are and how full the food pen is (if the food pen is still allowed to work). Sucks to be you, shouldn't have broken the rules. The longer the ban, the higher the chance that more pets will die. If the ban is a month long (or something), more pets will die than during a three-day ban.
When the user comes back, if the ban isn't permanent, they'd have to move their remaining pets into their shop/showroom. A hassle, sure, but again, their problem for having broken the rules.
I think this is a good solution to the problem of having pets 'stuck' on banned accounts. The current system is punishing users who play fairly by denying them any chance to get a name that belonged to a user who was banned. Please consider this.