Coincidentally, I'm reading a book about calories and their impact on diets right now. It's called "Why Calories Count".
They talk about two experiments done on total starvation over several weeks.
In both experiments the subject lost a huge amount of weight in the first few days due to the release of water from glycerol, and release of salt (accompanied by release of water) from the kidneys. After that the subjects, despite having vastly different starting weights, both settled in to a 0.3kg/day weight loss rate, body fat being the primary source of energy and the breakdown of body proteins also contributing.
About the BMR, the author of the book says that after one to three weeks the BMR begins to reduce as the weight loss slows down the body's energy requirements. The result is that it takes less energy to support body functions.
The basal metabolic rate drops in direct proportion to to the loss in body weight.
That's the author's take. I have not read the study myself to check on it; but here it is.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1274154/
Now, I've always been suspicious of the claims of "starvation mode". Mainly because I've never seen it quantified, demonstrated, or explained in a way that really made sense to me. An arbitrary rate of weight loss where the body suddenly says 'oh no... that's too fast, I need to do something...' vs. a more gradual weight loss that is gentle enough that the body doesn't even notice it? It just never rang true for me.
I know I have some confirmation bias here, so if there are some studies that you can point me to that support starvation mode, I'm happy to read them.