Example code for running a VIP site behind a reverse proxy with a subdirectory. This assumes the proxy server can't rewrite the html, such as on CloudFront. Props to 10up / Dropbox for much of the code.

vip-reverse-proxy-with-subdirectory.php

<?php

define( 'PROXY_URL', 'https://mysite.com/subdirectory' );

/**
 * Map the mysite home page to the proxy subdirectory
 */
function mysite_map_home_page(){
  add_rewrite_rule( '^'. get_mysite_proxy_subdirectory() .'/?$', 'index.php', 'top' );
  add_rewrite_rule( '^'. get_mysite_proxy_subdirectory() .'/page/?([0-9]{1,})/?$', 'index.php?paged=$matches[1]', 'top' );
}
add_action('init', 'mysite_map_home_page');

/**
 * Replace Site url with the entered proxy url for mapping proxy urls
 *
 * @param $url
 *
 * @return string
 */
function mysite_filter_proxy_url( $content ) {
  $vip_url   = trailingslashit( get_site_url() );
  $proxy_url = trailingslashit( PROXY_URL );
  $content_reference = $content;

  if ( $proxy_url && false === strpos( trailingslashit( $content_reference ) , $proxy_url) ) {
    // We must replace urls that already have the subdirectory, as well as urls that don't,
    // (depending on how WP created the url)
    list( $subdir ) = explode( '/', trim( parse_url( $proxy_url, PHP_URL_PATH ), '/' ) );
    $vip_url_with_subdir = trailingslashit( $vip_url . $subdir );

    $search 	= array( $vip_url_with_subdir, $vip_url );
    $replace 	= array( $proxy_url, $proxy_url );

    $content = str_replace( $search, $replace, $content );
  }
  return $content;
}

add_filter( 'post_comments_feed_link', 'mysite_filter_proxy_url' );
add_filter( 'category_feed_link', 'mysite_filter_proxy_url' );
add_filter( 'category_link', 'mysite_filter_proxy_url' );
add_filter( 'day_link', 'mysite_filter_proxy_url' );
add_filter( 'feed_link', 'mysite_filter_proxy_url' );
add_filter( 'month_link', 'mysite_filter_proxy_url' );
add_filter( 'page_link', 'mysite_filter_proxy_url' );
add_filter( 'post_link', 'mysite_filter_proxy_url' );
add_filter( 'year_link', 'mysite_filter_proxy_url' );
add_filter( 'the_permalink', 'mysite_filter_proxy_url' );
add_filter( 'tag_link', 'mysite_filter_proxy_url' );
add_filter( 'term_link', 'mysite_filter_proxy_url' );
add_filter( 'comment_url', 'mysite_filter_proxy_url' );
add_filter( 'the_content', 'mysite_filter_proxy_url' );
add_filter( 'get_shortlink', 'mysite_filter_proxy_url' );
add_filter( 'get_pagenum_link', 'mysite_filter_proxy_url' );
add_filter( 'redirect_canonical', 'mysite_filter_proxy_url' );

/**
 * Home URL that is replaced with the proxy url if it exits
 *
 * @return string
 */
function mysite_home_url( $path = '/' ) {
  return mysite_filter_proxy_url( home_url( esc_attr( $path ) ), false );
}

/**
 * Return proxy slug
 *
 * @return string
 */
function get_mysite_proxy_subdirectory() {
  return 'mysubdirectory'
}

/**
 *  Filter all the rewrite rules to include the proxy base slug
 *
 * @param $rules
 */
function mysite_proxy_rewrite( $rules){
  $new_rules = array();
  $proxy_subdirectory = get_mysite_proxy_subdirectory();
  foreach ($rules as $rule => $rewrite) {
    if ( false === strpos($rule, '^' . $proxy_subdirectory) && ! strpos( $rule, $proxy_subdirectory ) ) {
      if( '^' === substr( $rule , 0, 1)  ){
        $rule =  substr_replace($rule, '^' . $proxy_subdirectory . '/' , 0, 1);
        $new_rules[$rule] = $rewrite;
      } else {
        $rule = $proxy_subdirectory . '/' . $rule;
        $new_rules[$rule] = $rewrite;
      }
    } else {
      $new_rules[$rule] = $rewrite;
    }
  }
  return $new_rules;
}
add_filter('rewrite_rules_array', 'mysite_proxy_rewrite');

/**
 * Fix pingback header
 *
 * @param $headers
 * @param $this
 *
 * @return mixed
 */
function mysite_filter_pingback_url( $headers, $this ){
  $headers['X-Pingback'] = mysite_home_url( '/xmlrpc.php' ) ;
  return $headers;
}
add_filter( 'wp_headers', 'mysite_filter_pingback_url', 10, 2);

/**
 * Map sitemap.xml to match proxy
 *
 * @param $url
 * @param $path
 * @param $orig_scheme
 * @param $blog_id
 *
 * @return mixed
 */
function mysite_sitemap_proxy_urls(  $url, $path, $orig_scheme, $blog_id  ){

  //If the path is not for the sitemap.xml return the $url.
  if ( false === strpos( $path, 'sitemap.xml') ) {
    return $url;
  }

  $vip_url   = trailingslashit( get_site_url() );
  $proxy_url = trailingslashit( PROXY_URL );

  if ( $proxy_url && false === strpos( $url, $proxy_url) ) {
    // We must replace urls that already have the subdirectory, as well as urls that don't,
    // (depending on how WP created the url)
    list( $subdir ) = explode( '/', trim( parse_url( $proxy_url, PHP_URL_PATH ), '/' ) );
    $vip_url_with_subdir = trailingslashit( $vip_url . $subdir );

    $search 	= array( $vip_url_with_subdir, $vip_url );
    $replace 	= array( $proxy_url, $proxy_url );

    $url = str_replace( $search, $replace, $url );
  }

  return $url;
}
add_filter( 'home_url', 'mysite_sitemap_proxy_urls', 10, 4);

/**
 * Replace preview url with original VIP url
 *
 * @param $preview_link
 * @param $post
 *
 * @return mixed
 */
function mysite_vip_preview_url( $preview_link,  $post ){
  $vip_url   = trailingslashit( get_site_url() );
  $proxy_url = trailingslashit( PROXY_URL );

  if( 'draft' == $post->post_status || 'auto-draft' == $post->post_status  ){
    return str_replace( $proxy_url, $vip_url, $preview_link );
  }

  return str_replace( $proxy_url, $vip_url . get_mysite_proxy_subdirectory() . '/', $preview_link );
}
add_filter('preview_post_link', 'mysite_vip_preview_url', 10, 2);

// Disallow all direct crawling - bots should use the robots.txt on the main site
add_filter( 'robots_txt', function() {
	return "User-Agent: *\nDisallow: /";
});