The production of bile when fasting is debateable or let's just say the amount of bile which is produced. According to everything I've read bile production during fasting is reduced enough that liver flushing is recommended after a long fast since the lack of it's production causes conditions in the gallbladder/liver favorable for the production of stones,
The passing of stones during the MC is veeery rare thing and in the 6 +/- years I've participated in this forum on and off I only recall of 2 people claiming to be passing "actual" liver/gallbladder stones which is yet to be confirmed by at the very least these folks cutting the stones open to see if they are green on the inside which would indicated bile.
From the rare occasion of these occurences I would say that passing liver stones during fasting is probably due more to a condition of the particular individual than it being a matter of course reaction in fasting. The only other person I recall that claimed to pass stones during the MC was also dealing with a big tumor or ovarian cyst. I don't exactly recall which or even it it was what I mention but I do distinctly remember that it was some kinda major malady.