Posted in the Misc section because I'm not going to write enough for the Ideas section.
What if Billy and Mandy's hamster became a hollow? Renji or some other shinigami arrives and is forced to become their friend forever. You could have them live in Karakura town or not, whatever. I picture the fateful limbo contest being interrupted by a hollow, and the shinigami defeats it only to realize he touched the pole and must now be Billy and Mandy's servant.