It is generally treatable. You can soak the necklace in the mixed solution of baking soda and salt for several hours, then gently brush it with a soft brush for a few times, and then rinse it with clear water to remove the oxide on the surface.
If the oxidation phenomenon is serious, you can send the necklace to a professional store for maintenance. If necessary, it can be properly re-electroplated and polished to maintain the original color of the necklace, but daily maintenance and protection should be done to avoid affecting the luster of the surface.