Just to play devil's advocate: I think a fattie who suddenly decided to stop eating altogether would be diagnosed as having anorexia nervosa.  Of course they would eventually reach a low weight or die of malnutrition (or more likely, get the fuck over it after two days and start gorging themselves again) but anorexia is strictly speaking about your food consumption, not your weight, so it's theoretically possible to be fat-but-anorexic for a short period of time.  Whether it's actually psychologically plausible I'm not sure.