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There actually is an example of a human subpopulation that will go extinct due to not reproducing: https://en.wikipedia.org/wiki/Sabbathday_Lake_Shaker_Village

Your argument about sub populations can be just as easily applied to humans as a whole. Perhaps humans will be replaced by another species.

If you look at nature more coarsely, you don’t see population stabilization. Instead you see speciation and extinction due to random and constant changes. Perhaps there will be an environmental event that we would otherwise survive that will do us in because of our low population.