I'm creating a species of beings that are able to eat part of themselves when they are starving.
In a sense, Earth animals do this already by putting on fat. When there is a shortage of food, they can burn fat and keep going.
However, I'm looking for a plausible reason that my creatures cannot lay down internal fat. This means that, in times of need, they have to chew off a part of their external body. Luckily, when food becomes available again they can regrow the missing parts.
What prevents these creatures from evolving the equivalent of fat?
This shouldn't affect the existing answer by @DKNguyen. I thought it might be useful to describe the general body-plan of these creatures.
They are carnivores. Superficially they have a similarity to centaurs, i.e four legs and two arms. The body has the flexibility of a leopard's and the legs have claws instead of hooves. The hands have two opposable "thumbs" and the digits also have claws. The head is reminiscent of that of a Rugops https://en.wikipedia.org/wiki/Rugops. The tail is lizard-like but not so heavy as that of a bipedal dinosaur because it is not needed for balance in the same way. The tail is useful in making tight turns when chasing prey.