Anode: If there’s an excess of cations in solution, oxidation of the anode will slow down, then eventually stop. According to Le Chateliers Principle (LCP), the reverse reaction would be favoured in order to decrease the concentration of cations. Therefore, emf decreases.
Cathode: Reduction of cations at the cathode leads to an excess of anions in solution. Therefore, reduction of cations will slow down, then eventually stop. According to LCP, the reverse reaction will be favoured to increase the concentration of cations and counteract the excess of anions. Emf decreases.