I don't know about doing HIIT on an empty stomache. I usually just do light cardio on an empty stomache and HIIT later in the day. Because of the intensity I'd think you would lose some muscle doing it on an empty stomache even if you eat something afterward. HIIT works based on a metabolism spike, not what you burn during the excercise. Maybe it works if you have a slow metabolism, but I can't imagine doing HIIT on an empty stomache and not losing muscle.