The tests on Shri Prahlad Jani brought this seemingly impossible thing and something that could be brushed aside considering it as a quackery into mainstream discussion a few years ago. Please check this (or alternate link here) for a report on DIPAS (DRDO) study. Shri Prahlad Jani is said to be living without eating, consuming liquid and excreting.
In the book, “Autobiography of a Yogi”, Shri Paramhansa Yogananda writes about Smt. Giri Bala who was considered as a yogi who did not eat and who was tested by Maharaja of Burdwan for this ability. From the book it appears that she did not consume liquid also and would not have bodily excretions.
While Shri Prahlad Jani is not seen too much himself in the media teaching people about the technique, there is Shri Hira Ratan Manek who is actively sharing a technique for the same. Shri Manek himself has been reported to have fasted for long periods by surviving on just sun energy and water.
Going by the ancient texts pertaining to the variants of, “Tratak” and third eye meditation techniques, and with the above case studies, the possibility of living without eating can be explored.