I would still suspect that she lost her toe tips from frostbite or injury, or it is a birth defect. She should do well with her problem, but I would check her feet often to make sure that she isn't rubbing the hide off, or suffering from an infection.
One of my hens tore her nail off jumping over a chain link fence. After it healed, it was just as you describe--rounded and no nail. Another scenario is that she could have had frostbite on the toenails, and the rips fell off. Lastly, it could be a birth defect. Pictures are welcome.