For example:
Content of server-a.com/test.php:
echo 'hello world one';
// now I need to call server-b.com/test.php here silently
// without interfering with user experience
echo 'hello world two';
Content of server-b.com/test.php:
mail($foo, $bar, $qux); header('location: http://google.com');
Now running server-a.com/test.php should output hello world one hello world two. And it should not redirect to google.com even though server-b.com/test.php was called successfully.
server-a.com/test.php, you also silently runserver-b.com/test.php