Lower eyelid surgery does not address hollowed eyes. The surgical technique is designed to avoid them after removing fat by repositioning the remaining fat. However, if your main concern is gaunt looking eyes, blepharoplasty surgery is not going to correct them. Occasionally, blepharoplasty with fat transfer is used when there is extra skin and hollowing. Dermal fillers or fat transfer are generally considered the best options for correcting hollowed under eyes.