I figured that was the problem with Sneaky. My son's mother had a cat like that. She told me that her cat had belonged to a guy she worked with who bragged about starving the cat and letting his dogs go after her. She convinced the guy to give her the cat, who was a really sweet cat, but psychologically messed up.
Her cat would eat until she puked, then eat more. My ex had another cat, too, and the abused cat would attack him and steal his food! She had to feed the male cat separately, and the female was given small amounts of food all through the day to ensure she got enough to eat without getting sick from overeating.
A funny thing about this was that my son's mother also had a pet rat and a mouse. They were in cages on top of a tall file cabinet, and the female cat would sit on the ground all day and stare at the two rodents while smacking her lips and drooling all over herself!