The same thing happened to Japan a few decades ago. It's also happened to Korea more recently.
When your country is poor, moving to the U.S. offers great opportunities for you and your children. But as your country gets richer, the difference shrinks. At some point, you might find that your home country offers the same or better opportunities for you. As soon as the kids go to college (or get married), the parents are free to go back.
Too many elderly people coming back, though, could cause strain on a country's pension and welfare system. After all, they've never contributed anything toward a pension plan in their home country. Some people intentionally keep their old citizenship (even after decades of living in the U.S. and multiple opportunities to apply for U.S. citizenship) just so they can claim pension and welfare when they go back. Their lack of U.S. citizenship also makes them less emotionally attached to their new home and less involved in the public life of the U.S., making them even more likely to go back.
Worth mentioning: the US and Japan, as well as most first-world countries, have "totalization agreements" to take care of this. If you've paid into US Social Security for your entire working career and then retire to Japan, Japan pays you (fairly) equitably, and this is net out against e.g. me working for my entire career in Japan and then drawing US Social Security. (This includes two major question marks, like whether I'll be in the US at retirement and whether US Social Security will be worth enough to justify a postage stamp to get it.)
When your country is poor, moving to the U.S. offers great opportunities for you and your children. But as your country gets richer, the difference shrinks. At some point, you might find that your home country offers the same or better opportunities for you. As soon as the kids go to college (or get married), the parents are free to go back.
Too many elderly people coming back, though, could cause strain on a country's pension and welfare system. After all, they've never contributed anything toward a pension plan in their home country. Some people intentionally keep their old citizenship (even after decades of living in the U.S. and multiple opportunities to apply for U.S. citizenship) just so they can claim pension and welfare when they go back. Their lack of U.S. citizenship also makes them less emotionally attached to their new home and less involved in the public life of the U.S., making them even more likely to go back.