Earlier quoted context omitted.
> This is the way cultures and people have changed since time immemorial. Yeah, because some empire came and killed your people off and conquered your lands and enslaved your survivors and erased your culture so they could replace it their own. Not because people wiped themselves off the map because they wouldn't have children.
Cultures are and always have been constantly shifting and changing; conquest is one method of that happening, as you point out, but is far from the only one. Immigration, emigration, catastrophe, technological progress, climate change... all result in the movement of people and the shifting of national and cultural boundaries. No culture is "erased" as a result of this. Even if Japan fails to have children, Japanese…
No. Nations are a collection of people with shared ethnicity, land, culture, language, history. If the japanese people disappear, the nation will also disappear. It's not going to magically continue just because the country of Japan is still there. Can't have a nation without its people.