Unfortunately, it is unlikely that fat (from further back in the eye) will move forward over time. In fact, you should expect more fat loss and hollowness with increasing age. Too often, surgeons remove all the fat around the eye in an attempt to achieve a more "dramatic" result. This can leave the patient looking "skeletonized" and sunken. This problem can be treated with fat injections using donor fat taken from your abdomen, hips or thighs. The fat is injected using a small blunt cannula and takes only a few minutes. Alternatively, you can use one of the popular HA fillers. Find a surgeon with experience with fat injections and the treatment of hollow eyelids.