For an insoluble salt, MX, usually a solubility product, K_(sp), at some particular temperature, we can write the normal equilibrium expression:
MX(s)rightleftharpoons M^+(aq) + X^(-)(aq)
As for any equilibrium, we can write the equilibrium expression,
[[M^(+)(aq)][X^(-)(aq)]]/[MX(s)] = K_(sp).
Now normally, we have some handle on [X^-] or [M^+], but the concentration of the solid material [MX(s)] is meaningless and irrelevant; it is arbitrarily treated as 1. So,
[M^(+)(aq)][X^(-)(aq)] = K_(sp).
There may often be a precipitate of MX(s) in the bottom of the flask, however, this is completely irrelevant to the solubility product, and to the equilibrium. It is out of the game as a precipitate. [X^-], may be artificially raised to some extent as well (i.e. by introducing beforehand a soluble salt of X^-; such a procedure is called "salting out"). If M was a precious metal (say gold or rhodium or iridium), you would want to precipitate all this is out as an insoluble salt, as opposed to washing it down the sink.
