Exception traps in Stream Processing model

As I understand, the stream processing creates a second stream that will be ingested back through the various process layers of fluent-bit. I'd like to understand the recommended way to use stream processing to branch to various outputs BUT also include an exception trap or catch-all route so that any events not matching the stream condition are routed to a remediation destination.
I can't currently understand how to achieve this - in my tests the default output also caught the 'selected' messages, not just the exceptions. (i.e. the non-stream path also included the stream path data instead of just the non-stream data).
Could this be included in the 101 example?