I'm not sure how they track illegal aliens that they've opted not to export just yet, but by definition, once they are in the system by way of intentional interaction with the government, they are "documented". Becomming identified/identifiable is far from impossible; Its an inconvenient pain though.

All it takes to get a library card is a piece of mail. For that mail, an address. Homeless shelters(among others, but here its free of charge) provide address/mail services(of a sort, and by request). Library card + piece of mail plus some sort of birth certificate(think a foreign one will do) will get you a State ID, generally issued at the DMV/BMV, but you don't have to pass a driving exam for an ID.

Getting ID alone is not the problem. The problem is all the baggage it un-packs into a mess on the floor. IMHO, someone who takes the initiative to literally tell the government who they are and where they live should be allowed to work, rent an apartment, recieve healthcare, and otherwise be left alone unless they need help or commit a crime ... hell, make them citizens after x years "above board" ... but that's not the state we live in.

"Work Permit"/"Visa"/whatever, should come with some guarantees/privileges/obligations(for any party bring an immigrant/potential in), like, thanks for letting us know you're coming, here's your job, some necessities/food and a place to stay until you can afford better. Whenever we hit the point that NOT having those things meant illegal/criminal is one of the tipping points where the US became less free. I don't care what an idividual has done, that damage to our Liberty and the promise of "The American Dream" was worse, no matter your criteria.

Immigmants bring prosperity and good will. Always have and still do(todays immigrants, especially the illegal ones, are more law-abiding than any before), regardless of legal status. There is no reason to treat them as our government does today.