You shall obviously set up monitoring of the MQ and all its DLQs. Once you've done that, you will literally never have a failing processing flow that isn't caught. A successfully initiated Mats Flow will either run to completion, or it will DLQ. Guaranteed.
The MatsBrokerMonitor is a Mats-specific such monitor (compared to the generic monitor ActiveMQ comes with). The pages here are a bit lacking, but it at least explains a bit: https://mats3.io/docs/matsbrokermonitor/