Well, pretty much by definition when the average EROEI<1 then energy production does stop.
Can you point to a real-world case where that actually happened?
Yeah:

Easter Island.

They ran out of trees (=fuel for fire).

They applied a match to what was left of the "woods", namely to the ashes. The ashes wouldn't catch fire. EROI of the lit match was less than unity. So production stopped. Most of the population died-off.

The End.

We don't really produce energy, we convert it from one form to another (ex: from heat to mechanical force). Having an EROI < 1 is not a problem as long as you can rely on another source of cheap energy (slaves, cheap gasoline or electricity).