How long would it take to lose weight if burning 1000 calories per day and eating 300?

First of all no human should ever subject themselves to that kind of diet. That is a boderline anorexia. The amount of calorie intake should be nothing less than 1200. But to answer your question, it depends on how much energy you exert that day. Your body runs off calories like a car runs off gas. If you don't exercise or sit on the couch all day you aren't going to burn anything that you eat. I would suggest talking to your doctor, depending on your current size, weight, age and current eating habits it will be easier to make an exercise program that will work for you without putting an extreme amount of pressure on the body.