A very low-calorie ketogenic diet (VLCKD) is characterized by low daily caloric intake (less than 800 kcal/day), low carbohydrate intake (<50 g/day) and normoproteic (1–1.5 g of protein/kg of ideal body weight) contents.
Your VLCKD sounds like a protein-sparing modified fast...
Atkins and other ketogenic diets often start with 2 weeks of
eating no more than 20 gms. of carbs a day until ketosis is established and weight
is being lost every day. After the 2 weeks you might add 5 gms of
carbs daily for a week, if weight is still being lost, add another 5 carbs a week,
keep adding and weighing until your desired weight is reached and is stable.
Then maintain your weight at this level with no additional level of carb eating
for life.