Loads of topics here about that...
There is heaps of info here and online about the potential dangers of eating such a low calorie diet. Like a car your body needs fuel to perform, this includes losing weight. 200 calories a day is starvation, plain and simple, and if done long enough you will do very serious damage to yourself and require professional treatment and/or hospitalization.
Many people out there sadly think that starving their bodies means they will burn fat faster. In fact the opposite is true. Once the body begins starving it will slow down the fat burning process or stop it completely in order to keep you alive longer. Instead you begin burning muscle. Then once the hunger kicks in you will end up overeating and gaining back all the weight you lost, plus more. The truly sad part is the weight you put back on is fat, the weight you lost would likely be muscle.
All in all, as has been said so many times, starvation is not the key to success in weight loss. A healthy diet and exercise is the only way to achieve long term success. 200 calories a day is a fools game which not only leads to failure, but could also cost you big bucks in medical treatment later, if not your life.
As a person who has known people personally who havebeen hositalized due to stupidly low calorie diets, believe me, it isn't worth it. Ever.
That aside however, if you are talking doing it one day a week or something like that, I suppose there are many people in the world who also believe fasting one day a week is very healthy for you and does not do permanent damage. I agree with this to a degree. The only problem I see with the "every now and then" 200 calorie a day approach is kind of like drinking. 1 drink every now and then easily turns into more now and less then. If you believe the 1 day a week of fasting (or 200 calories) is helping, it may become too easy to turn that into 2 days, 3 days, then ahh what the hell, all week..... Thats when the trouble starts. For the record, most people fasting 1 day a week are doing so for religious or faith related reasons, not weight loss. Once again the slow and steady method of weight loss is the clear winner. Everytime.
sirant