Answer
The equilibrium would favor the products, dissolving more of the $PbCl_2(s)$ into $Pb^{2+}$ and $Cl^-$ ions.
** The solid $PbCl_2$ would lose some concentration, but $AgCl(s)$ would be formed.
Work Step by Step
This is the equilibrium reaction:
$PbCl_2(s) \lt -- \gt Pb^{2+} (aq) + 2Cl^-(aq)$
When we add $AgNO_3$, the $Ag^+$ ions will react with the $Cl^-$ ions, producing $AgCl$ (which will precipitate).
Following the Le Chatelier's principle, since we are reducing the concentration of one of the products, the equilibrium will try to raise this concentration, to reduce the change.
Therefore, the salt will start to dissolve, because the equilibrium moved to the right.
