For an insoluble salt, MX, usually a solubility product, Ksp, at some particular temperature, we can write the normal equilibrium expression:
MX(s)⇌M+(aq)+X−(aq)
As for any equilibrium, we can write the equilibrium expression,
[M+(aq)][X−(aq)]MX(s) = Ksp.
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)] = Ksp.
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.