Muscle is a lot easier for your body to break down than fat. Muscle is also where amino acids are stored in your body. When you fast you are depriving your body of the amino acids it needs on a daily basis, and which it normally gets from your food. Fat storing is an end result of generations of adaptation to times when there wasn't a grocery store or McDonalds on every street corner. Fat is conserved for when it is truly needed.

Ketosis happens when you starve yourself as well. Some fat is burned, but so is muscle, during starvation. When LCing you are restricting carbs but you are also providing protein and fat as nourishment, so your body does not need to look to an inner source of amino acids.

It will, to a certain extent. VLCD (very low calorie diets) are as close to starvation as you can get w/o actually fasting. They provide great results for the first few weeks, then the losses slow down and often come to a halt. The body adapts to less calories and metabolism slows - but this takes weeks. "Starvation Mode" doesn't happen in 4 days.

HTH
Nat