A theoretical study of a quenched-annealed system where both components were modeled as charge symmetric +1: -1 primitive model electrolytes is presented. The adsorbed model electrolyte, mimicking lithium chloride solution, was assumed to be in thermodynamic equilibrium with an external reservoir of the same electrolyte. This partly quenched system was studied by applying the replica Ornstein-Zernike (ROZ) integral equation in the hypernetted chain (HNC) approximation and the grand canonical Monte Carlo technique. The effects of the concentration of matrix ions, pre-quenching conditions, and the electrolyte and solvent conditions on the adsorption of electrolyte were examined. The results indicate that the mean activity coefficient of the adsorbed electrolyte may differ substantially from the value of the corresponding quantity in the equilibrium bulk solution. The concentration of the annealed electrolyte in the matrix can be higher (sorption) or lower (rejection) than the corresponding equilibrium bulk concentration, depending on conditions of matrix preparation and on the temperature of adsorption. An important observation of this study is that the ROZ/HNC approximation can be solved for very high couplings, i.e., we can obtain valid results in the region of parameters where the regular OZ/HNC, applied to the equivalent bulk electrolyte solution, fails to converge. The agreement between the computer simulations and ROZ/HNC results for the adsorption isotherms is good.