The equilibrium is possible when there is no exchange of matter between system and surroundings.
At equilibrium state the forward and backward processes occur with same rate (speed)
When a system reaches equilibrium at a given temperature, the forward and reverse reactions are occurring at the same rate, and the concentrations (or partial pressures) of the reactants and products no longer change with time. At this point, the system has achieved a steady state, where the rate of the forward reaction is equal to the rate of the reverse reaction. So when equilibrium is attained, the value of all its parameters became constant.
The solubility is function of solubility product, the value of which is constant at a given temperature.