windchime, obviously people can starve to death. The point isn't whether one can starve to death but what strategies the body's metabolism uses to try to hang on.
As calories slip lower, the body's mechanisms notice!

So metabolism switches into conservation. This means slower metabolism and holding on to fat reserves. Many people have experienced a halt to weight loss and even a weight gain if they are consistently eating a lot less than they are burning. If this state goes on too long, yes, one will lose weight and ultimately die.
There is nothing magical about 1200 calories. Someone who is very heavy can have their body switch over to conservation if they eat less than 1800 cals. or even more. Someone who is exercising excessively to try to burn a lot more calories can also go into this stall state.
1200 calories is considered to be the lowest amount one can eat and still get enough nutrition from food, assuming one is eating a balanced diet (and not 1200 calories of candy). Nutrition means protein, carbohydrate, fat, and vitamins and minerals. To go to less than that, one should be under medical supervision. Some medical weight-loss programs do go to fewer calories, but the person is being given specific supplements, and they have tests done regularly.
As people lose weight, they are not losing just fat. The body is happy to burn muscle as well, because it's easier to break down protein for energy. The reason physical activity/exercise is suggested is that it helps lessen the amount of muscle breakdown, and it also increases metabolism. Muscle is the primary tissue that burns fat for fuel.
The basic idea is to avoid extremes...
Jay