But that’s what’s happening now. The new generations in the developed world are not reproducing, so they will not have descendants. Unless something changes, the culture will be replaced by one that produces descendants.
You are not using “people” in the same sense. I mean “people” as a national culture, which does shift from generation to generation, but generally not in a radical sense. Immigrants assimilate over time, although they do leave lasting influence on the culture as they merge with it. Families pass on aspects of their attitudes and beliefs. Generations pass on cultural knowledge through media. This is why millennial culture in the US is a continuation and evolution of Boomer culture, despite all the intergenerational strife.
As the culture is replaced, revolution and/or national disintegration becomes more likely, as there is little to unite people in the face of significant challenges. (Why should I sacrifice for neighbors I can’t relate to? Why should I follow the laws and cultural codes of a nation I have no deep connection to? Perhaps my own culture’s standards are better!) It’s a natural process that’s happened many times throughout history.
(This sounds overly cut and dry, but culture is complicated, and a national culture is made up of tens to hundreds of regional cultures and subcultures that all have a share of influence. In the end it’s an abstraction. You can’t really force a culture of any size to behave in a certain way, nor can you “preserve” it except in the form of documentation. But culture does produce a lineage of identifiable characteristics that gets passed down, if it survives.)