alt Hacker News> the city's foreign born population has been stable for at least 15 years
This statement doesn't contradict the one about international immigrants keeping the city from shrinking. It is easy to imagine how immigrants come to NY, give birth to natural born Americans, who then move out of the city. This process can come to some kind of a dynamic equilibrium with a stable population of foreign born people.
Not only that, when an international immigrant to the city later moves out of the city, like my cousin’s family did, that’s also counted as domestic migration.