Set cache headers on WordPress 404 pages.

functions.php

<?php 
/**
 * Force cache headers on 404 pages and prevent WordPress from handling 404s.
 *
 * @param bool $preempt determines who handles 404s.
 * @param obj  $wp_query global query object.
 */
function change_404_headers( $preempt, $wp_query ) {
	if ( ! is_admin() && ! is_robots() && count( $wp_query->posts ) < 1 ) {
		header( 'Cache-Control: max-age=30000, must-revalidate' );
		header( 'Expires: ' . gmdate( 'D, d M Y H:i:s', strtotime( '+5000 minutes' ) ) . ' GMT' );
		header( 'Last-Modified: ' . gmdate( 'D, d M Y H:i:s', strtotime( '-5000 minutes' ) ) . ' GMT' );
		$wp_query->set_404();
		status_header( 404 );
		// prevents the default 404 from firing.
		return true;
	}
	return $preempt;
}
add_filter( 'pre_handle_404', 'change_404_headers', 2, 99 );