Building muscle on a calorie deficit is possible for most people. When it comes to the human body which is one of the most complicated biological organisms on this planet, I can't help but shutter when I hear people give such overly simplified answers and these people are usually wrong. your body uses the following energies in order of preference 1. carbs 2. fats 3. protein. When the body operates on a reduced calorie intake it will draw on reserves mainly body fat and to a degree protein. Fat is in essence the body saving energy for a rainy day and will draw calories from it when not fed enough to cover the calorie defecit, that is the only purpose the body stores fat. when this happens other things happen to the body, it becomes more effecient by burning less calories as well as other things such as a taking more time to heal it self. the longer you remain on a calorie deficit or if you all ready carry a small body fat percentage then your body will attempt to break down your muscle and vital organs to feed it self. usually most Americans are in little danger of having that happen. unless you suffer from a eating disorder. But generally the body treats muscle tears as it would treat any other injury and repair itself. The body has this thing called self preservation and will do what it can to live and repairing torn muscle fibers is one of them. So basically yes most people are capable of building muscle while dieting especially if you are walking around with 20 percent or more body fat. Is it easy? No way! Can it be done? yes! Hard work and taking more time to heal between work outs and a protein supplement is also needed, while the body can break down a pound of fat to provide 3500 calories, it can not naturally produce protein. This is still under simplified but i can be here all day and confuse some people needlessly..