hook_menu_site_status_alter() has been removed

As of Drupal 8 hook_menu_site_status_alter() no longer exists.
The equilavent way of altering the site status in Drupal 8 is by implementing an event subscriber and giving it a priority between 30 and 40
This way you make sure that the _maintenance key is set in the request attributes and the maintenance theme is not invoked yet.

Of course if you dont want to alter the site status, but just to apply custom logic in case the key is TRUE (eg sending an email) your subscriber should fire with a weight smaller than 30

D7

/**
 * Implements hook_menu_site_status_alter().
 */
function mymodule_menu_site_status_alter(&$menu_site_status, $path) {
  if ($menu_site_status == MENU_SITE_OFFLINE) {
    // Do stuff.
  }
}

D8
In your modules mymodule.services.yml

services:
  mymodule_maintenance_mode_subscriber:
    class: Drupal\mymodule\EventSubscriber\MaintenanceModeSubscriber
    tags:
      - { name: event_subscriber }

/**
 * @file
 * Contains \Drupal\mymodule\EventSubscriber\MaintenanceModeSubscriber.
 */

namespace Drupal\mymodule\EventSubscriber;

use Symfony\Component\EventDispatcher\EventSubscriberInterface;
use Symfony\Component\HttpKernel\Event\GetResponseEvent;
use Symfony\Component\HttpKernel\KernelEvents;

class MaintenanceModeSubscriber implements EventSubscriberInterface {

  /**
   * Does something.
   *
   * @param \Symfony\Component\HttpKernel\Event\GetResponseEvent $event
   *   The event to process.
   */
  public function onKernelRequestMaintenance(GetResponseEvent $event) {
    $request = $event->getRequest();
    if ($request->attributes->get('_maintenance') == MENU_SITE_OFFLINE) {
      // Do stuff.
    }
  }

  /**
   * {@inheritdoc}
   */
  public static function getSubscribedEvents() {
    $events[KernelEvents::REQUEST][] = array('onKernelRequestMaintenance', 35);
    return $events;
  }

}