This isn't a theoretical - most of Western Europe has been in this boat for a long time, and relies heavily on immigration to fill the labour gap (despite however much political posturing about wanting to restrict immigration)
If we do this on a global scale, there is nowhere to draw immigrants from, and a bunch of old folks are going to be abandoned to die...
The problem I have with this logic is that it seems to assume a binary of the population either staying at least as high as it is or massively reducing. The idea that there's no middle ground where the population goes down slowly rather than massively spiking all at once feels like it needs much more justification rather than just assuming it.
https://www.economist.com/interactive/briefing/2025/09/11/hu....