Hi Dean,
Interesting question!
It’s certainly possible to do that, however it’s something of a custom development task and so I’m afraid we can’t go into too much depth on this one.
The simplest path, though, might be to try and detect if there are no upcoming events and, if so, pull in the past events with an appropriate piece of text explaining that to the visitor, ie:
We don’t have any upcoming events right now, but check out these previous events for examples of what we get up to around here!
…Or, whatever makes sense in your case – this would just help to avoid confusion amongst visitors. To learn more about tribe_get_events() (the function you would probably use to pull in those past events) and theming in general, check out these resources:
I hope that gives you some ideas 🙂