What horsecrap. When the Irish came to America, they came on slow ships on a one-time lifelong trip, to become full Americans.
Many. many, of the 19-th early 20th immigrants went back. About 1/3 of Italians, I believe. A lot of the posters here respond to any correction by saying "Yes, but illegal is different from legal." That's true. But it doesn't justify assertions about the past that aren't true.
Let's argue today's policies (and I may agree with you). But let's not rewrite the past.