Retracted nostrils can be both congenital (born with that particular shape) as well as a result of previous nasal surgery. The nostril rim (ala) is anatomically weak (lack of cartilage support) and has a tendency to "retract" or "notch" if not properly treated. Patients who possess this prior to any surgery are at a high risk for worsening after surgery and preventative measures are often best.
The treatment is variable and frequently depends upon the specifics of the problem, how much skin remains and if there is sufficient cartilage within the nose to correct the issue. It is not uncommon to go a step further and use rib or ear cartilage as a source of additional grafting material in "secondary" or "revision" surgical cases.
Regardless, both are acceptable techniques to correct this problem, and a secondary discussion with your surgeons may help you understand why one technique makes more sense in your particular case. Communication is one of the most important factors you must have with your surgeon prior to any cosmetic surgical procedure. And, ensure that the surgeon you choose has significant experience with secondary rhinoplasty, as it is the most challenging of any cosmetic surgical procedure.
Vincent Marin, MD, FACS