Our BMR is the result of a number of factors, one of which is the amount of tissue we have to maintain, so one thing that lowers BMR is losing weight. That is certainly a good thing.
Another thing that lowers BMR is calorie restriction. If we diet by cutting calories, the body responds by lowering BMR to match, which makes losing weight more difficult, which means we have to go even hungrier in order to continue losing, which makes the body reduce the BMR further, and so forth. I think it is clear why most people consider this a bad thing.
The way Dr. Fung explains it, as long as there are calories coming in, the body adjusts to suit the intake. If we fast, on the other hand, the body simply draws energy from stored fat and keeps the metabolism going without altering the metabolism. The corollary of this is that if the body is reducing BMR, it’s going to want to hold onto its stored fat for as long as possible, to keep us going in adverse circumstances. If the body is increasing BMR, on the other hand, it becomes willing to use stored fat as well as dietary fat, which is one of the reasons that a well-formulated ketogenic diet helps to normalize our weight by allowing excess stored fat to be metabolized. (This is all in the absence of carbohydrate, of course, since stimulating a high level of insulin secretion creates an entirely different hormonal ball game.)
Off the top of my head, I would say that if you stop having your period from eating too little, or your hair and fingernails stop growing, or you are in your pubertal growth spurt but your growth is stunted, these would all be signs of not getting enough calories for your daily minimum needs. I’m sure there are other signs, as well.