An obese person will die of malnutrition as opposed to pure starvation in case of lack of food. If all the proper nutrients are provided, including basic proteins and fats, but not a single carbohydrate nor any extra protein or fat that can count as energy, the obese person will lose weight. They will lose weight really fast. At 700 lbs we’re talking a few lbs a day. Starvation mode or not your body can’t pull energy out of thin air. Yes, your metabolism will become very efficient and your energy levels will shoot to hell, but with even 100% efficiency that is forbidden by the laws of physics you still need a baseline amount of energy to continue life, and if that energy does not come from without it will either come from within or you will die. No ifs or buts. Of course, the less you weigh the less energy you need.
Here’s a rough mathematical explanation:
Assuming your overall metabolic efficiency factor is represented by S which is somewhere between 0 and 1. Your input energy is the stuff you eat we can represent with I and your energy requirement is E. Now, let’s call net energy deficit (i.e. energy you spent on everything but did not consume) L. The basic metabolic formula becomes
L = S*I - E
However, these are not numbers, although theoretically they are quantifiable values, in reality they are functions of a few interdependant variables. We do not know these functions and it’s probably not very possible to completely determine them but we can make approximated functions by figuring out relationships and approximate coefficients.
Now, S, your efficiency, is a function of your food intake, genetics, hormonal levels, activity and who knows what else. Your intake can basically be considered everything you eat but it’s reasonable to attribute digestability to intake and not to general efficiency. So your intake is the part of food that you digest. Now your E, your energy expenditure is a function of your body mass, lean body mass, activity levels, and probably a lot of other factors as well.
Now, starvation mode is when your intake I starts approaching 0 due to either lack of food or lack of digestion, your efficiency is raised to compensate and minimize energy deficit. However, if you notice, even if your efficiency was 1 (and it can’t exceed 1 due to those pesky laws of thermodynamics) an I of 0 means you are guaranteed to have some energy deficit, specifically -E. As your food intake drops to 0, E will drop due to low energy levels and general increase of efficiency. but E cannot drop to 0 since you need energy to sustain life function by definition.
Therefore, regardless of any particular details of your metabolic activity or any starvation mode it is impossible to avoid an energy deficit if your food intake is 0. Thermodynamically speaking it’s also highly unlikely your efficiency can change all that much - in the absolute best case you are using almost all of the food you eat. If you don’t eat any food that energy will have to come from fat reserves, muscle, organ tissues, or something.
Starvation might be dangerous in all sorts of ways but it is impossible to maintain or gain chemical energy in your body without shoveling it in your self somehow. Now the peculiarity comes in that since efficiency is related to so many things, sometimes eating slightly more than you are now can lead to a greater energy deficit (and hence greater weight loss).
IANAD, etc. Don’t try this at home.
Doctor dopers can probably fill in some of the functions and variables above with actual relationships ( I would expect most of them to be positive bell curves with varying coefficients ) and provide cites.