There has been endless discussion on where soft stones come from, so I will add to that endless debate.
One theory is that they form instantly at any point in time when the bile is not balanced enough to keep the cholesterol in solution. Background, bile consists of several components, but basically bile salts and cholesterol. Bile salts keep the normally solid waxy cholesterol in solution or liquified, if there is not enough bile salts the cholesterol will solidify (which would later form a ball shape) . So imagine at any time this imbalance could occur somewhere in the liver and form a plug stagnating the bile and reducing detoxification from that portion of the liver. For all we know the liver could be forming the stones (or to a greater extent) during the Liver Flush itself as if there was ever a time to create an imbalance and shortage of bile it could be during the liver flush. The liver then might catch up and force this ball out once the bile becomes liquid and balanced once again.
This is just regarding the soft stones, not the hardened ones that are commonly found. Really the debate is inmaterial for those looking for health benefits of purging the liver and not for those trying solely to purge stones. Therapeutic effects of the liver can be achieved regardless of stone purging. Which means that even if the stones were olive oil soap(which they are not) it wouldnt matter as you are still purging toxins and hardened stones both of which achieve the intended goal which is relief from a condition.