And all the while this is happening your economy is getting wrecked not only because suddenly you have far fewer people, but because your society turns into a giant retirement home, as fertility also determines the age ratios within a society. You can see this by working backwards. Again taking a fertility rate of 1 as an example, if we have 1 newborn then we have 2 20-40 year olds, 4 40-60 year olds, 8 60-80 year olds, and so on. So you have a shrinking economy paired alongside an even smaller ratio of workers, and much greater social strains on that economy as well.
This is also why immigration isn't anything more than a very short-term bandaid. When you're speaking of population declines near 100% over such small windows of time, you end up needing to basically replace the entire population of a region. Doing this with immigration, let alone as this is increasingly a global crisis, just isn't realistic. And this is completely ignoring the social consequences of such actions.