Here is how I would do it:
function save_extra_user_profile_fields( $user_id ) {
if (!isset($_POST['address']) || empty($_POST['address'])) {
// this field was not set or was empty
// do your action
wp_redirect( home_url() ); // or profile page
exit;
} else {
// field was set and contains a value
// do your action
update_user_meta( $user_id, 'address', $_POST['address'] );
wp_redirect( home_url() ); // or whatever success page
exit;
}
}