Bin Pets were added in The Binscape update as pets. They could be bought at the Bin Pet Shop for 5000 Mulch, but were only for Bin Tycoons (when one's tycoon mebership expired, the Bin Pet vanished and went to a Bin Pet Hotel).
During the 2012 Makeover, Bin Pets became buyable to anyone through Dosh, and did not vanish if Tycoon membership expired (however, there was a bug that meant people who ahd lost Bin pets were unable to purchase new ones as a message nformed them that their pet was still in the hotel. This has since been fixed).
The Bin Pet is stored on the website as a nest object, and when it in the Hotel or Not visibale it doesn't update, meaning that it may be possible to do the Big Weevil Trick with a pet. Pets ahev two attributes, hunger and fitness, and training increases fitness and decreases hunger, whilst feeding has the reverse effect. The pet can juggle up to five balls and do a variatae of tricks via imitation ot training.