Assuming the purpose of this hypothetical situation is to eat as much as you want without gaining weight – Calories are generally not the main factor for weight gain. The real factors consist of: most grain products and trans fats, and lack of saturated fats, the latter especially if the diet includes a lot of protein . It doesn’t really matter how many calories you eat, what does matter is what you get those calories from.
As well… If you get zero calories from your food, you’re going to die within a few weeks regardless of how much you eat. Carbohydrates and fats can be converted to calories, but according to this situation, you would get zero calories from those as well.
Still, for the sake of being on-topic – I wouldn’t start eating anything in particular, I’d just stick to my regular diet. Being able to eat more doesn’t appeal to me, especially when the only nutritional factor that is ignored is caloric intake.