[simplestats]

Birth rates are predicted to keep going down though, meaning the supply of immigrants will dry up anyway.

[ashtonkem]

It won't though. The UN's models on the area say that world population will continue to grow (population has momentum) until the end of that century, at which point population growth will be very close to 0, with an estimated population of 10.5 billion people. So even in total numbers, we won't run out of people anytime soon.

Even when global populations begin to fall, we can still keep immigration up. There's nothing at all inconsistent with falling populations and immigration. Economically there might be a lot of pressure for people in places with falling populations to emigrate, because of the economic effects of sudden population drops.

[oblio]

There's about 6.5 billion people (and that number is growing!) in developing countries.

You're safe for at least 50 years.