What I see though are governments which oppress their people to the point of illness, the way abused animals stop procreating — and then rather than confront that behavior in themselves, buy replacements they subsequently abuse the same way.
But ignoring that, the end result is the same whether people can't or won't figure out how to do it: immigration is an increasing necessity, and as more and more countries tip below replacement it will lead to increasingly desperate measures to compete for it.
With respect to oppression, the two most consistent factors correlating with falling birth rates is higher education and increased wealth.
A manual laborer start to get productive at 16, and stop after 50, depending on his form.
So basically, you avoid paying for his education, he is productive right away, and with some luck, he will retire in his country (or the state may deport him) and die there.
Not saying it's good, but that's the way the world work right now.