Currently, there's no feature like a Pound yet, but it's being worked on so it will definitely become available in the future.
As for the event, currently the ligers are the only pets. You can gather tokens from the crow (who's sitting on the sofa in the room in the hat) every 15 minutes, with which you will be able to obtain pets later on in the event. Every day, more pets get released and there may be some items among the releases as well. Also, Niles (the dog in the room in the hat) might also give us pets later on in the event, or at least conversation options.
Basically you just check the NPCs every day to see if there's anything new to talk about, collect tokens every 15 minutes from Abaddon and trade those tokens for pets.