I know the plot, but my character’s shouldn’t.
A character who is fated to die, should have the same level of character development (motivations, hopes and dreams, fears…) as a character who will live to the end of the novel, or through a series. In most cases you want the character’s death to be a surprise and jarring to the reader, and so you want to do the best you can to hide the plot twists before they happen.
I especially like the idea of foretelling a plot twist, but keeping it so obscure that the “signs” are only seen in hindsight (i.e. like in my short story The Captive). On a similar vein, it would also be interesting to have a character who shows all the “symptoms” of I’m-going-to-die-soon, but then lives on.
If the character is undergoing a personal crisis, that doesn’t mean that everyone else in the world is aware of it and leaves them alone. Life goes on, and those not aware of the plot would behave normally. However, this must be held in contradiction with “if it doesn’t move the plot along, cut it”.