Robert Zubrin's space elevator book analyzes this situation and concludes that most of the mass would either escape or burn up in the atmosphere. Only the bottom-most section would hit the ground.
His design contemplates anchoring to a movable ocean-going platform, both for this kind of safety issue and because it means you can steer it away from big-but-easy-to-track tropical storms.
His design contemplates anchoring to a movable ocean-going platform, both for this kind of safety issue and because it means you can steer it away from big-but-easy-to-track tropical storms.