If you go to low you can actually not have enough carbohydrates to actually burn fat. Fat oxidations requires substrates from the krebs cycle. If your deficient in these area's your body looks for other sources of energy. Which can come in the form of Amino Acids. AA usually account for about 4 % of total energy production under normal circumstances. So as Magic stated timing your nutrient intake is important.
Secondly insulin enhances the hormone Leptin. Low insulin cause Leptin to be undersecreted by adipose tissue. The consequence of low leptin levels is that it puts the body in starvation mode, which is not what you want at all.