There's no mechanism by which your body can suddenly start using less energy to do the same thing. If there were, it would do that all the time.
I just noticed I didn't reply to this line. This is factually incorrect and seems to be the basis for your entire misconception. Your body will absolutely use less energy once it starts dipping into its fat stores. After 3 days with no carb intake you will definately go into a very light form of hibernation as your body doesn't want to burn its reserves. This is backed up in numerous scientific studies. The first hit on google "Effects of dieting and exercise on resting metabolic rate" gives the quotes:
"However, the determinants of energy expenditure, specifically resting metabolic rate, are an active area of research with many debatable issues...Caloric restriction is known to produce a short-term reduction in resting metabolic rate..In the first part of the study, subjects' resting metabolic rate decreased to a greater extent than their weight or fat-free mass. This excessive reduction is most likely attributable to the degree of calorie restriction, and therefore cannot be completely explained by the reduction in fat-free mass."
This is a long established fact in nutritional science. Here's a meta study -
"The authors searched the literature and found 22 studies between 1984 and 1995 that documented resting metabolic rate in humans placed in either diet-only groups or diet-plus-exercise groups. The studies represent data from 631 subjects, 68 males and 563 females, 31–45 years of age. The majority of studies placed subjects on low-fat, high-carbohydrate diets of less than 1200 kilocalories per day. Most subjects were involved in aerobic exercise for 31 to 60 minutes, 4 or 5 days per week at an intensity of about 50–70% of maximum aerobic capacity. Intervention programmes lasted approximately 10 weeks. Effect sizes for differences in resting metabolic rate before and after diet and before and after diet-plus-exercise were calculated. When expressed in absolute terms, there was a significant decrease in resting metabolic rate in diet only (283.4 ± 32.2 to 253.5 ± 34.5) and diet-plus-exercise groups (279.6 ± 36.4 to 255.5 ± 34.2)."
10 weeks was not enough to lose much weight so it's not a case of "there's less of you so you you less energy", yet BMR went down 250-300 calories per person because of the sub 1200 calorie diets. Their mode exhibited a starvation response and they burned less passive energy whether they were working out or not! They had to work out just to offset the adaptive thermogenesis effect. The metabolic difference in a 1000 calorie diet and a 1500 calorie one are not insignificant.