The answer is yes and no, but probably not in the way you intend.
The first answer is from thermodynamics: the creature cannot gain more energy from eating the tail than it expended growing it. In fact, due to the inefficiency of metabolism, you will gain quite a lot less.
Then again, nearly every creature alive does this on a regular basis. Mind you we don't engage in coarse measures like gnawing on our own limbs. We can do this much more efficiently with chemical signals. Catabolysis occurs when the body decides to consume its own tissues to survive. This is actually happening on a constant basis with fat cells. Through lipolysis, fat cells are constantly shedding their energy rich fats so that the body may consume it. In more extreme situations, we'll even turn on our own muscles, harvesting them for the protien to survive.
I doubt this sort of chemical reality is what you were looking for. However, consider butterflies and moths. When the caterpillar is born, it has no use for its protective egg shell anymore... but it has valuable nutrients in it. The caterpillar turns around and eats its own egg before going out to chew on the leaves. So this may be an example of a part of the caterpillar, its egg shell, which gets cannibalized because it is no longer needed.
Which leads to one case I can think of where you might actually see a pattern like you describe. There may be a symbiosis of two creatures, like corals and the algae they hold onto. The algae give corals extra energy in the form of sugars, and the corals protect the algae.
However, this balance can shift. When a coral is stressed, such as due to rising ocean temperatures, it "bleaches," expelling all of its symbotic algae into the ocean. This makes it turn white because a large portion of the color of the coral came from the algaes.
You could develop a similar symbiotic relationship. During normal times, the host provides a platform for some energy producer (or other valuable role). This energy producer breeds during times of great plenty. In times of strife, the host may decide that it can no longer provide the nutrients the symbiote needs, and turn on it, consuming it for fuel. As long as the symbiote's lifecycle dovetails with this nicely (I'm thinking something interesting like the jellyfish lifecycle) the symbiote species will not be "offended" by this, and patiently wait for the environment to support the host better.