Notification for failed payment transaction
The answer depends on the Payment Processor you’re using. We have that option in the iATS Payments Extension and we can do that because its recurring payments are initiated/controled from within CiviCRM. 

If you’re using another payment processing that processes a recurring contribution off-site and then notifies CiviCRM you will likely have to get into that Payment Processor’s admin/config and look for such a notification option.