When the durability of the elytra wings is used up, the icon appears as a random item. Each time the world is exit and reentered, the icon changes to a different icon entirely. Only once did it show the correct icon.
This can be recreated in creative mode by turning on cheats and entering the command:
'/give @p elytra 1 431'
The number 431 represents the durability of the elytra used up.
Furthermore, when the broken wings did display correctly, the wings with full durability appeared broken as seen in the last picture.