I know personally this happened often in the 80s' My Brasilian friends did exactly that--they became nannaies and whent he BF came up they got pregnant, then they had to leave for personal reasons and could only come back thru their "American" child.
Until our government recognizes and DOES SOMETHING about illegal immigration that will WORK, it's still a reciprocal fee. When there was no fee, our Brasilians brought their children and just less than $10K each to deposit in US banks because of 300% inflation on their money. They did this every opportunity they had. Was it smart? For them--yes. We then paid inito the IMF to bail out BRasil more than once--now Barackhas given them drilling right for our OIL. SOB. one-termer.