Quick question. Why not just add the content to Stream 1? After all, they won't get it until they've exhausted the content above it anyway.
If there is a reason why you want to do it in another stream, you could create a Smart Campaign that runs nightly or weekly (depending on your cadence) to move them. The filter would be as pictured. The flow would be "Change Engagement Program Stream".
I would ask why is there the option to add other streams? Ie what is the point? My first stream is a program I carried over from nurture that was previously setup so it's not exactly in the engagement program format. If I do add content here, is Marketo smart enough to send the new stuff to the exhausted leads?
I have the filter, but I need to add a trigger for the new stream to activate. Have no clue what that trigger would be. Was looking for something like 'exhausted stream 1'.
The reason you may want to have additional streams is because you might want to nurture leads by different stages.
E.g. Early Stage - Leads that just entered into your system
Mid Stage - Leads that are Marketing Qualified Leads
Late Stage - Leads that become opportunities
Yes, the Engagement Program is smart enough to know when there are new pieces of content and if leads haven't already received that piece of content they will have it send at the next cadence.
You cannot create triggers for exhausted leads, but you can create an external recurring batch that moves people who are exhausted using the filter Mike mentioned above.
Hope that helps! :)