It is not uncommon for saints, those with highly advanced states of consciousness, to stop eating. They grow out of the need for material sustenance. A teacher of mine, Swami Bua, subsisted on a tiny bit of vegetable juice each day and died—nobody really knew his exact age—definitely over the age of 115.
How do they do it?
Why do they do it is also a good question.
In more elevated states of consciousness, the act of digesting food is disruptive to the experience, takes away from it, pulls you out of it. Consider why fasting has always been tied to the concept of spirituality. This is the primary reason why the act is given up. It's also a subtle argument in favor of a light, plant-based diet—it takes away from the experience of elevated consciousness less than a heavy, meat-based diet.
The science behind the how, I doubt can fully be explained with the written word. These Great Souls have realized the irreality of reality. The game nature of everything you see, touch, taste, smell, hear. Their consciousness then quite literally pulls out of time (past-future), the defining feature of five-sense reality—and they rest in the Eternal Now.
With awareness fixed and rooted in the Eternal Now, there is no forward motion of time as we typically reckon it, there is no effort, no stress, no disease. The aging process slows dramatically, as the awareness has a profound impact on the physical body. We have historical accounts of saints living 500+ years—when you consider the genius of the physical body and its resiliency, it doesn't seem conceptually outlandish.
Living in a kind of state of suspended animation, hunger does not really develop, as all systems are fed by the bliss and fullness of the moment.
It's good, at least, to know about the possibility.