TYPO3 Core

For the frontend, there is already an "end-of-frontend-rendering" hook that is called shortly before output is started. Is that enough for your purpose?

1 TYPO3\CMS\Core\Core\Bootstrap::run("typo3/")

/var/www/html/developer/typo3_src-7.3.1/typo3/mod.php:

00022: define('TYPO3_MODE', 'BE');
00023: require __DIR__ . '/sysext/core/Classes/Core/Bootstrap.php';

00024: \TYPO3\CMS\Core\Core\Bootstrap::getInstance()->run('typo3/')->shutdown();

A hook could be added here.

    /**
     * Things that should be performed to shut down the framework.
     * This method is called in all important scripts for a clean
     * shut down of the system.
     *
     * @return Bootstrap
     * @internal This is not a public API method, do not use in own extensions
     */
    public function shutdown() {
        return $this;
    }