Japan will survive as a people and culture as long as they dont start importing culturally backwards savages like europe is doing.
Their population my dip down, but it will stabilize.
Europe is commiting cultural suicide for sure.
And historically, no known society has been able to pull out of such a severe dowanward fertility spiral. None.
In a couple of generations, in a "One-Child-Glorious" society, each and every child has 2 parents, 4 grandparents, and 8 great-grandparents all to him or herself. And no brothers, sisters, uncles, aunts, or cousins.
Do you think any such child, with eight great-grandparents to care for (either directly, or through taxes) is going to decide in their 20's or 30's to get married and have kids?
No, Japan will not "stabilize." Nations which will not reproduce, are replaced by those who do.