Yes.....the mechanism of fat burning must be understood. For fats to be converted to citric acid, oxaloacetate must be available. Without oxaloacetate, citric acid cannot be formed and acetyl-CoA cannot be further processed.
Oxaloacetate can be produced from the breakdown of certain amino acids. However a person on a high fat/low carbohydrate/low protein diet, or no food, will need to use the oxaloacetate for gluconeogenesis.
Fatty acid breakdown however must still occur for ATP generation and acetyl-CoA will need to be processed through an alternative pathway. This pathway leads to the formation of ketone bodies.
The amino acids will need to be derived from muscle tissue, leading to muscle wastage.