Low-Carbohydrate High-Fat Metabolism
When you eat fat, it's turned into fatty acids, which in the absence of insulin, becomes acetyl-CoA, and CAN"T become fat in your body. The fat you eat can't (there are some tiny exceptions) become glucose.
While fatty acids might supply almost all your energy, glucose is also being used, perhaps immediately after eating, and continually to supply some glucose to the brain and the central nervous system. Some dispute exists about how much glucose the brain needs, but if you are producing ketones, insulin is off, and the glucose supply to the brain may less that 60gm per day. (30gm a day some say.)
Fatty Acids for Energy
Dietary fat has to be disassembled in the small intestine into free fatty acids, which are then small enough to pass through the intestine wall. Fatty acids in the blood are readily accepted by all the bodies cells except the red blood cells, the central nervous system and the brain.
Long chain fatty acids (from fat) are also converted to acetyl-CoA, by a process called β-oxidation, which occurs inside the mitochondrion. Acetyl-CoA enters the citric acid cycle from there. (Also called the TCA cycle or the Krebs Cycle)
Fatty Acids as Building Blocks
Free fatty acids are also needed to build hormones and cell tissues. Essential fatty acids can only be obtained by dietary means.
In either starvation, or the absence of dietary carbohydrate, with an excess of fatty acids in the system, the liver uses β-oxidation to make acetyl-CoA, and converts that to make the ketone bodies, β-hydroxybutyrate and acetoacetate. β-hydroxybutyrate and acetoacetate are transport agents for acetyl-CoA.
Your muscles, the heart, the brain, the central nervous system, prefer to use ketones for fuel if ketones are available. The effect of that preference is that ketones are readily accepted by all body cells including the brain whenever possible. Since the brain and your heart and muscles prefer to use ketones, glucose which is scarce, is spared. In other words, the body saves glucose for the important job of sustaining the constant glucose level in the blood.
The presence of ketones conserves glucose and expends the more abundant triglycerides. In the same way since glucose is spared, there is no emergency requiring the breakdown of protein to make glucose. Hence protein is spared too.