Many illegals use bogus SSN's, apparently colleges don't bother to check, or aren't required to. Some banks and other institutions are accepting matricular cards now, only illegal aliens would need them.
The whole system is turning into a scam, one set of laws for the lawbreakers and one for the rest of us.
Hard to say. Foreigners can get a U.S. taxpayer identification number, which is really exactly the same thing as a social security number. If that person ever immigrates here, that is their social security number. Legally (although perhaps not enforced) this number is required for VA benefits -- for example, if you are the foreign national spouse beneficiary of a government life insurance policy taken out by your deceased GI husband, you are supposed to get a number.
However, this is a good question to raise. When you apply for a number, don't you have to provide your nationality? And did these people tell the truth about that?