The "anchor baby law" (the one that used to let children born in the U.S. keep their illegal parents with them) was repealed during the Clinton Administration. Under current law, children born in the U.S. to illegal parents cannot sponsor their parents for citizenship until the child turns 18. So the parents can be deported, and have the choice of taking their kids with them or putting them up for adoption. But the children are U.S. citizens, are entitled to a U.S. passport, and can come back when they turn 18.
Which wasn't the case until Brennan slipped it in as a footnote on a case in 1982. Even Harry Reid said it was a ridiculous idea and tried to fix it until he realized that floods of poor people coming into the country would only benefit the Democrats.