Much like the question here about reptilians hosting the news, I thought that there could not possibly be people who would make claims like this.
However, some searching proved me wrong.
While not particularly prevalent, there are more than a few people out there making the claim that they can survive (and remain perfectly healthy) for sometimes up to 70 years without any food and water. However, apparently not all can achieve this degree of success, and claim various ranges. Some claim that they live solely on light and air.
For the record, there are some who call themselves "breatharians" and some who call themselves "inediates". I am not sure which is the preferred term.
They include pages like this as "evidence" for their claims.
Some are kind enough to be willing to give their secrets freely to the public as a pdf filepdf file which they encourage the reader to share freely, since presumably the author has no need to waste his income on trivialities such as food or a monthly water bill. However, there are others who offer classes for $10,000 USD, but throw in immortality as an added bonus.
I found that the "Breatharian Institute of America" also spouts a rapid-fire Gish gallop of other claims but I want to limit this question to just the scientific evidence as to:
Is it possible to live while remaining healthy, without eating or drinking for these extreme periods of time?
Has any particular individual making these claims been subjected to scientific study?
I know that this is (pun intended) low-hanging fruit, but I haven't seen the question addressed here yet.