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 culture and the Japanese nation will continue. It will look different, certainly. But there's nothing magical or better about the way things used to be simply because they used to be that way. Change is inevitable, and more than that, it is good.