Is there a calorie minimum below which people should not go?

When you eat less than about 1,200 Calories you risk nutrient deficiencies. Remember, the foods we eat provide lots of nutrients, and even if we need to lose weight our bodies still need nutrients like vitamins, minerals as well as protein, carbohydrate, and even fat. The 1,200 minimum does not mean everyone should eat 1,200 calories to lose weight. In fact many people will lose weight on 1,800, 2,000 or even higher if you are very active or have a lot of weight to lose. Eating any less than 1,200 Calories may also be too restrictive and may cause you feel “diet deprivation backlash” which is unpleasant and causes many people to abandon a diet before they even have a chance of success.

Your minimum or maximum calories allowed depends upon your demographics like age, height, weight, health conditions etc. You need to consult a registered dietitian or your physician/health care provider before you follow any calorie restricted diet. 

In general, women should not consume less than 1,000 to 1,200 calories per day and men should not consume less than approximately 1,800 calories per day. However I like to take an individualized approach since every person and every situation is different. These minimums are typically very uncomfortable for most people so rather than giving minimums to everyone I believe it is best to find out each person's calorie requirement and then scale back from there depending on what changes they are willing to make.