Using LeChatelier's principle, why doesn't BiCl3 dissolve with water?

Question

In class, we did a bunch of experiments to apply LeChatelier's principle. I get that the equilibrium wants to go towards the direction with the least effects of the stress, but how does this apply to BiCl3 not being soluble in water? When we added HCl, it dissolved because BiCl3 dissolves under HCl, and HCl is soluble in water because of the hydrogen and its ability to break up ions. BiCl3 was solid - a white powdery crystal. When we added more water after adding HCl, it got cloudy again. So water + BiCl3 = precipitate.

Answer 1

BiCl3 (s) + H20 (l) <=====> BiOCl (s) + 2 HCl (aq) (hydrolysis reaction)

BiOCl is insoluble in water, but when excess HCl is added, the equilibrium is shifted to the left to produce more BiCl3 which is water soluble. Adding H2O drives the reaction to the right again, precipitating BiOCl.