Thats what I did.
Weighted the pop ratio 50000:1 in favor of males, so there are so few females that they die out after a single generation.
But every time the civ should die it gets repopulated with a fresh batch "from unknown parentage".
Like this:
Just in case it matters, what I wanted to do was create a civ that has sole access to overpowered weapons (and only those) and can create artifacts. They should stick around for about 50 years, create a dozen or so legendary weapons (since those are the only moodable things they can produce) and then die out. By the time world gen stops those weapons would hopefully be spread all over the world, with no possible way to produce more.
Think the Wheel Of Times heron blades or the shardblades in the Stormlight Archieve for examples of what I want to accomplish.
Back when all members of civs were explicitly modeled, it was possible to do this, but the changeover to abstract populations broke it. The game now appears to assume that all civilizations are capable of reproduction, resulting in the behavior you observed if they actually aren't.
I was not able to come up with a new scheme for assuring that a civ goes extinct.
If the pop limit tokens work again (those were also broken by the pop changeover) it's possible you can create a civ that has only one or a few sites, and is therefore PRONE to dying out during world gen (Lowering the Biome support values might also help this), but there would always be some chance of them surviving.
I believe you can make a civ that is essentially guaranteed to starve (make them agriculture-dependent and start in a biome where agriculture doesn't work), but I think that happens instantly, with no chance to create artifacts.