I shouldn't say “once in the States,” as that sounds too immediate. I should say, once they have been in the States long enough to learn the ropes, learn how to hide for a while after they have over-stayed their visas, and have found the loop-holes in the immigrations system.
In the case of the the Chinese man of whom I was very personally aware, he worked with the girl, and both got separate visas, obviously without the US Embassy in Beijing able to make any personal connection between the two. The man, who was a student of mine for more than two years, told me seriously, thinking I wouldn't care, that he and the girl intended to procreate in the States, make an anchor baby, and never go back to China. It was a business arrangement between them.
Having first-hand knowledge of the plot, and knowing I had to be in Hong Kong within days of hearing his plan, I intended to turn the man and his “business partner” in to the authorities. I did report it. That's when the Consulate in HK informed me that they already figure a percentage of people who have just such (and many other kinds of) intentions. They were not even interested in taking the man's name.
Visa overstays are a huge problem. No question about that.
If two aliens procreate in the United States and have a citizen baby, that does not mean they get to stay in the United States. The baby won't help them at all until he or she turns twenty one, at which point the baby could then apply for visas to get his or her parents in. If a foreign student marries a citizen, that's a different matter, but making a baby with another foreigner won't keep him in this country.