Shutdown functions not working on php-fpm setup?
Example shutdown is getting called ; you can't use dpm in a shutdown function though, because at that point the session already got written to the database and there's just no way to add a new message to it.

In PHP-FPM, the connection also could have already been closed, so print or var_dump is not really a good test to check if you're shutdown function is getting called in general ; it should work in D7 though if you're not using a module that's specifically closing the request, so you should be able to use print "Hello world"; and get it to show on screen (that's what the core "Shutdown functions tests" is doing in D7).

If you want something realiable to use in a shutdown function to check if it got invoked, try something like file_put_contents('/tmp/drupal-debug.txt', 'Shutdown function called');