Undocumented, as we all know, doesn't mean someone who's lost his papers, but an illegal, who never had legal residence in the first place.
- There’s a lot of debate on what we call these people. Some say “illegals” is too harsh. Then there’s “undocumented worker.”  What is that? I left my wallet in Mexico?
If you left your driver's license at home, you are "undocumented:" if you're driving without a license, you're a criminal. 
I remember hearing a story about a detective who was asked for spare change by a vagrant.
He showed the guy his badge, and aked him for his ID, and the vagrant said "Er, sorry, I left my wallet on my dresser at home."
The cop said "I've heard that so often,  that sometimes I think there's a dresser somewhere in this town with a pile of wallets on it three feet high."
He was wrong: it's in Guadalajara.