If you're not a US citizen but have a child in the US, Will you be shipped back?

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First off, I was born and raised in the United States. I am a United States citizen as well as everyone in my family but a discussion arose when non-US-citizens, get pregnant and have a child in the United States, what happens to them? Will they have legal rights to say in the United States since their child was born in the America? I heard before, that was true but since a lot of people are doing that, they banned it? How do you feel about people wanting to stay in the US? I think it's nice to have a diverse world but United States just isn't big enough to hold everyone..