While it is true that someone can eat 500 calories and lose weight, this will not be allowed to happen for an entire three weeks. The body will only allow this to occur for 3 to 5 days at which point it will go into survival mode. This will be apparent by the lack of energy and an increase of hungry to the extreme. It will include hunger headaches and weight loss would stop. The body would then begin to turn everything eaten into fat stores. The body will not allow this situation to last for longer than 5 days without doing something to force the person to eat. In the event that the person refuses to eat, the body goes further into survival mode and slows the metabolism.
The body was not designed to thrive but to survive. When we use the "traditional" weight loss methods, (like extreme exercise and reduced calories), weight loss is indeed possible; however it often comes directly from lean muscle mass and the essential structural fat. That is why it is very common for people to regain the weight once returning to "normal eating". They will also gain a few additional pounds because the body is trying to create an environment for survival. The same is true when diuretics and other weight loss pills and powders are used.