Hello, I made this account pretty much just to ask this question, and I didn't think this was very plot-relevant, so I assumed it was okay not to include "spoiler" in the title.
Regardless, when I buy my old eye from Barkis in the Smoldering Corpse Tavern, I can opt to replace it, or let it rot. Letting it rot does nothing, and replacing it kills me. But when I look online, it looks as if I'm supposed to get experience, some history, and a bonus for this eye. None of that seems to happen, or is at least announced to have happened.
It would seem that you just have very little HP and as tearing out the eye causes a little damage, it simply kills you. I haven't heard of anything else that could cause this.
When you compare a game to Oblivion, God kills a kitten.