What does it mean for a country to not survive? There will be people there. There will be a system of governance. Sure, there will be hardship and suffering, but I don't see how this equates to extinction.
Yes, probably not people extinction. But economic extinction - the tiny amount of young supporting 10x the amount of elderly will lead to economic collapse. On top of the collapse in raw productivity. It’s not hard to imagine that level of disruption leading to a failed state scenario.