Killing was an extremely very poor choice of words on my part, as this certainly doesn't have to involve death. Take South Korea as a contemporary example with their publicized 0.7 fertility rate. That trends towards extinction at an exponential pace. But now imagine there was another group within South Korea that started going the opposite direction and just having massive numbers of children.

You could even create an equilibrium level (probably more theoretic than practical at the population levels in modern times, but not necessarily in ancient) where this group's fertility trends up end perfectly balancing against the rest of South Korea's low fertility trends, such that the population doesn't even meaningfully change, or maybe even increases, yet the DNA pool ends up near to 100% controlled by a tiny minority. I'm curious if and how this would look different (from a long distant DNA analysis) from the suggestion that suddenly all of South Korea just mysteriously died and these were the only people left.

Interesting idea. But this would require no intermixing between groups.