The most common cause of rounding of the lower eyelids is a subciliary blepharoplasty, a surgery where an incision is made below the eyelid. When skin is removed in an attempt to tighten it, the weak lower eyelid pulls down, causing a rounding of the eyelid with a loss of the almond eye shape. If you look closely at many subciliary blepharoplasties, there is some alteration in eye shape. this typically shows as rounding of the eyelid or pulling down in the corners, producing a downward cant or sad appearance.
This problem can actually get worse over time as the natural weakness of the lower eyelid increases over time.
Fortunately, in most cases, this condition is treatable. It is best in my opinion not just to perform a canthopexy (or canthoplasty, depending on the looseness of the lower eyelid), but also to do an advancement of the cheek tissues (a cheeklift). This "gives" tissues to the lower eyelid which can then be used for reconstruction of the lower eyelid. Our version of the cheeklift is the USIC, or ultrashort incision cheeklift (R). Often volume replacement with autologous tissue (or even with Restylane) helps as well.
A canthopexy alone can give a severe upward sweep to the lower eyelid that looks artificial. Likewise some cheeklifts, perticularly when they are performed from inside the mouth (subperiosteal) with a second incision in the temple tends to give an increased distance between the cheekpads (intermalar distance), so this should be anticipated before it is incurred. The lateral bunching of the eye must often be dealt with as well.
These surgeries are highly technical, so choose your surgeon accordingly. A special interest in the lower eyelid and the midface is a plus.
There are several articles and a book chapter in the textbook Mathes on this topic referenced below.