If a country's population does not reproduce, tautologically, it will die off. This is true in a sense, if you think of a country being defined genetically ins

If a country's population does not reproduce, tautologically, it will die off. This is true in a sense, if you think of a country being defined genetically instead of culturally. But assimilating immigrants into a culture is often considered racist too these days. So in a practical sense you are correct even if your basic premise is wrong.