I don't know exactly to what method you are refrring to.
Word fasting is almost always used to define eating very little or no food, usually no fats and no proteins.
If you are planing to go on fasting (fat free/protein free diet), you should know one thing:
Fasting (fat free/protein free diet) promotes bile stagnation, and bile stagnation promotes stones formation.
In other words, Fasting promotes liver stones
(intrahepatic) and Gallstones
Problem with bile stagnation while fasting can be solved by incluing special teas or remedies to promote bile flow, like teas made with bitter herbs, or like taking cofee enemas or Oil Enema
Also, taking a Liver Flush
after every 2- 3 weeks fasting will counter negative effects.
So, not only that fasting alone is not going to melt stones, but it may contribute to new stones.