They can't. The only power they have is the one enumerated in the Constitution to repel invasion and secure the borders.
Illegals are still people in the common or natural-law sense of the word. Without the creation of the legal entity via a birth certificate from one of the states, government has no jurisdiction and therefore no control until issuance of a visa, green card, or other form of official FEDERAL documentation.
They still persons according to law because they're illegals.
Before anyone yells about tinfoil, answer this-
'States' are defined in the codes as a 'political subdivisions'. A political subdivision is an artificial thing.
So how can a real, live human being be born inside something artificial?
My copy of the Declaration of Independence states, "We the people of the United States..."
What's the language in your copy, "We the illegal aliens that violated federal law by sneaking in from Mexico, Libya, Syria and every other nation that hates the United States..."?
LOL!