Good evening, and thank you for your question.
When a dog's pupil turns white, it is likely that you are seeing the lens which has a cataract. You can read more about cataracts here: http://www.animaleyecare.net/diseases/cataract.htm
It can happen in one eye, or both. It can affect the old or the young. They can turn white slowly or seemingly overnight.
I'm not sure why your vet was unable to diagnose this problem. This makes me think that it is not a cataract. Though it sounds like you are describing this. If your vet confirmed it is not a cataract, let me know and I'll see if I can find out a bit more to help you better.
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