If one were to eat only 300  calories per day for a week, how much weight would they lose?

Don't do it. No one should eat less than 1200 cal per day without medical supervision. Starving yourself makes you lose muscle and decrease your metabolic rate so in the end people often don't lose or rebournd.. Eat 1200 cal of fruits, veggies, whole grains and lean protein daily. Each pound of weight is worth approx 3500 calories, so if you burn off 2200 cal and eat 1200/day, you will lose 2 lb/week.