TFM often seems to endorse a low carbohydrate diet for weight loss
There is a minimum amount of carbohydrate needed for brain function. Go below that and your body starts destroying it's own protein to produce carbohydrate.
Any exercise above a certain intensity for a certain amount of time or longer requires carbohydrate fuel and in the absence of carbohydrate in your diet results in your body destroying it's own protein to produce carbohydrate or inability to exercise at that intensity
You can lose muscle and still gain strength because you lost weight and because of nerve firing adaptations
I should have talked about a no carbohydrate diet.
I would estimate if you eat 700 Carbohydrate Calories that is enough if you are sedentary to reduce protein breakdown
If you exercise you need a little more carbohydrate to prevent protein breakdown
If you go under a certain amount you will break down more protein but can still gain strength due to weight loss and nerves