I would want it to be as close as possible, but in the ideal world I would be working very closely with the screenwriter to make sure it was right.
I took a screenwriting class in college. When a screenwriter adapts a novel they essentially take then 10 most important scenes and fill in the rest with stuff that is mostly accurate to the original storyline. So if the 10 major scenes didn't include a character then that character essentially disappears from the movie.
I like Dremer's Hunger Games example. I heard a lot of people complaining that the movie wasn't accurate to the book, but the book was written in first person, something that is already difficult to adapt to the screen because nobody wants a constant voiceover of the character's thoughts. Second, nobody wants to watch a 4 hour movie of Katniss starving in the woods. So they picked out the major plot points and filled in the rest.