How Common Are Long-Term Effects of Blepharoplasty - Especially Sunken Eyes?

Lower lid blepharoplasty should ideally preserve most or all of a patient’s lower lid fat, unless there truly is marked excess that is bulging outward. Fat can not only be treated by removal – it can also be restrained, and it can even be repositioned into areas of hollowness such as the tear trough. In addition, fat can be added to areas of hollowness in and around the lower lids to camouflage or ‘correct’ adjacent areas of fullness. I frequently perform structural fat grafting of the lower lid / cheek junction at the time of lower blepharoplasty, to add lower lid support and to blend the contour of the lid and cheek.
Fat grafting of the lower lid area requires experience and meticulous technique. As the area is covered by a very thin layer of skin and muscle, overcorrection must be absolutely avoided. My approach is to graft fat to the point that the area looks aesthetically ideal, then stop and wait 3 months to assess fat survival. As fat survival is variable, additional fat grafting procedures may be performed based on the results of the first. In most cases of post-surgical lower lid hollowness, two to three fat grafting procedures are required to restore adequate subcutaneous fullness in this area. 

Current techniques are appropriately more conservative regarding fat removal as hollow, sunken eyes are a sign of advanced age.  In fact, you can ask your surgeon directly how much fat he intends to remove to get an idea of how aggressive his technique may be.  I have, at times, recommended adding fat by micro-transfers to bring back the fat of youthful eyelids with nice results.