There was a starvation experiment (google Minnesota starvation experiment) where people did go into "starvation mode" and their BMR did decrease.  But here's the kicker: they were actually starving, for a long time.    The data is a little tough to interpret without medical knowledge (physicist here, not physician) but it appears that the greatest decrease in BMR was only about 25%.    In other words, people who were literally starving half to death only had a maximum BMR drop of 25%.  The study notes there was virtually no difference in BMR until the subjects started to get quite thin.