Yes, surviving without food and water is not impossible if some cases are to be believed. Some of you might be aware of "Inedia" or "Breatharianism" where people believe that food and water are not necessary.
There have been many examples of people who have claimed it.- Jasmuheen (born Ellen Greve), Wiley Brooks, Hira Ratan Manek and the one case I am interested in- Prahlad Jani (also called Mataji) who claims he hasn't had anything for 70 years now and has never fallen ill!