Here's the scenario: Jorge hears of the ALIEN JACKPOT, gets a SSN, files a tax return and gets EITC of $2900 refunded (married filing jointly with 1 qualifying child). He also files returns for 3 previous years and gets another $8700 back. Jorge comes here to STSC and learns LEGAL NAME is different than True Name, that SSN was issued to LEGAL NAME person, not True Name. He wisely leaves the SS card at home.

Jorge, arriving at work smiling.
The Man: Nice wheels.
Jorge: Thanks
The Man: I heard there's some new IRS money available for immigrants.
Jorge: Oh
The Man: Yeah but you gotta get a Social.
Jorge: I see.
The Man: You got a social?
Jorge: No Senor. I no has social number.
The Man: Well then, it's still cash on the barrelhead.
Jorge: Gracias

Jorge knows that if he doesn't have the SS card with him, he can honestly answer: I have no Social Security number. The number was issued to the person, not him. He can chose to make a use of it, or not.