A couple of thoughts on the topic,..
1- losing 'fight' isn't the same as losing 'weight'
2- while your body can make carbs from protein, it can't make protein from carbs (or specifically sugars, or fats), which will drastically impact the maintenance of lean muscle when protein isn't being ingested (and once your body has scavenged all of your skeletal muscle tissue)
So I guess theoretically, so long as you were ingested enough protein to support current muscle tissue, even if only from protein shakes, which in turn will support your metabolism, and through some odd chance, you're getting enough healthy fats that your hormones don't take a horrible dip, it is possible. I imagine such a drastic choice for the majority of non-essential calories is sort of like IIFYM taken to extremes.
Remember though, when in a severe deficit, and without reasons to retain muscle, your body will burn through muscle quickly as it's "costly" to maintain. This is a very quick, and simple way to lose "weight", although I doubt you'll find many people on this site who would be willing to follow such an approach.