I understand conservation of energy, the problem here is that extrapolating from that to weight loss strategy is a specious argument. If you reduce the energy intake on a human you don't immediately start triggering fat burning: you can also trigger reduced effort expended (both directly, and a reduction in normal metabolic processes) as well as burning of muscle tissue (which won't help either). If the person in question is actually metabolically unable to burn their fat, then you will starve them to coma and then death. The energy as stored fat has to be present *and available for use* before they're going to get thin this way.
So *if* you can reduce their calorific intake and *if* you can maintain their energy output, it still might not be *fat* that's being consumed for the balance. Would you lose weight? Not necessarily: consider that the starvation may even cause retention of a low-calorie item (eg water) that could actually increase overall mass. Your body is not a fission reactor: E=MC2 doesn't apply here.
