Immigration Status of Abandoned Children?

What happens to kids of illegal immigrants if they are abandoned or left without guardians/caretakers?

For example, if a couple illegally immigrated from Canada to America with their four year old kid and the couple either die or something happens to them and somehow social services get a call for the kid, what happens to them? And no, I don't mean that the kid was born in the U.S, the kid too is illegal...

Do they become American citizens because they are in the state's custody? What if they have no family to deport them back to Canada? Do they have to go through an immigration process? What if the children are found with absolutely no papers?

I think they get used for science experiments in secret government labs.

Seriously, good question, don't know.

I am pretty sure they are considered US Citizens at that point. A friend of mine's grandmother was found in New York city when she was just over a year old next to a dead woman in a tenement who authorities can only assume was her mother. They were able to determine that the woman was not a US citizen, but my friend's grandmother became a ward of the state and was adopted out to an American family.

Of course this would have been within the first two decades of the 20th century, so laws may have changed since then.

send 'em back to a living relective. if none... send 'em back

This shows a humanitarian side of the USofA. I hope all countries would act this way. Sending them 'home' would be abandonment.
Some parents who want their children to either escape persecution or just have a better life, demonstrate an amazing love by so getting their children into England, usually via Heathrow, by 'abandoning' them without any documents. Their parents might well fear they would not get asylum as so many English think, or are reported as thinking, that England is accepting too many migrants.