Excess removal of fat from the lower lids can create a hollowed out appearance.
Your concerns are valid and you should choose surgeon who will conservatively remove the fat or redistributed to an area of need. Make sure that you see lots of pre-and postop photographs.
Lower eyelid blepharoplasty incision
The primary goal of lower blepharoplasty is to remove a conservative portion of the 3 fatty compartments in the lower lids. The lower eyelid fat is removed through a trans-conjunctival approach. This removes the puffiness look. When patients are over 50 and had excess wrinkles, then a pinch technique can be performed on the outside of the eyelids at the lash line. This incision is closed with tissue glue. isIn our practice there are no stitches used on the lower lids. For many examples, please see link below
Hollowed out look after lower blepharoplasty
A conservative fat removal using transconctival (inside eyelid) with or without skin pinch removal should not cause a hollowed-out look. It can greatly improve your eyes and take away the tired look that many patients have from puffy under eye area. Many times adding fillers to certain areas (i.e, tear trough) will better contour your lower eye area. This can be done 2-3 weeks after the surgery.
Hollow look after lower blepharoplasty
You are correct to be concerned. Over resection of fat from the lower eyelid can certainly create a Hollow look. You need to discuss this in detail with your plastic surgeon and insist that only protruding fat that is causing a puffy eyes or eye bags be resected and it over resection not be done.
In younger patients with no loose skin the trans-conjunctival blepharoplasty can be done without skin resection. However if you have any loose skin at all some skin resection may be required. This can often be done through a small incision on the side called a "skin pinch blepharoplasty". Please see your plastic surgeon again and discuss all of these details thoroughly. Once surgery is done at cannot be undone.
It can be difficult for surgeons to exercise restraint. The surgery is not a fat removal surgery. It is a eyelid sculpting surgery. For this reason less fat remove rather than too much fat removal is the correct approach. For this reason, arcus marginalis release surgery has become very popular where rather than removing fat, lower eyelid fat is moved to the top of the cheek to reduce the under eye hollow.