Which files can be replaced in a child theme?

For ie.css specifically, the issue is that it is included via get_template_directory_uri(), which will output the parent theme directory when a child theme is being used. The solution is to add an action hooked to wp_enqueue_scripts with a lower priority, dequeue the stylesheet, then re-enqueue it using get_stylesheet_directory_uri(), which will load it from the child theme directory.