Actually there are several well-documented health risks of rapid weight loss, especially these two:
Increase in cardiac arrhythmias and increase in chance of sudden heart attack with very-low-cal diets. This is because of a phenomenon that tends to occur late at night when the last glycogen stores of the day's meals are depleted; muscle proteins are then broken down to make more glucose in an effort to keep glucose stable for the brain. Unfortunately this muscle-breakdown process also includes cardiac muscle.
Risk of gallstone formation increases dramatically increases at higher rates of weight loss (esp above a loss rate of 3-4 lb/wk). Has to do with how the breakdown products of body fat are metabolized by the liver. Studies show this can occur in as many as 25% of rapid-weight-loss subjects. It happened to my sister. Incredibly painful and can require abdominal surgery and removal of the gall bladder, which then makes it difficult-to-impossible to digest high-fat meals for the rest of your life. It's not worth taking that risk.
Other complications can include: hair loss, fatigue, dizziness, muscle cramps and electrolyte imbalances, but the above 2 are the major concerns. Also, studies repeatedly show that very-low-calorie (VLC) diets do not produce greater or longer-lasting weight loss than slower-weight-loss diets (see here for a good review). So after six people died in the 1980s while following the Cambridge diet (<500 kcal/day), the U.S. medical community decided to recommend no more than 2 lbs/wk and staying above approximately 800-1000 kcal/day.