Do the math. A birthrate of 1.1 means the population halves every 30 years. That isn’t stability. That is collapse. If you were in a collapsing building, would you refer to it as “stable”? A massive elderly population’s mooching off a small young population taxed at oppressive rates is not a stable pattern.
Stable, developed nations have high inward migration along with longer lifespans and what not. They are not going to disappear anytime soon.