[swiftcoder]

Keep in mind that "undocumented" is a term-of-art. They may in practice be extremely well documented, in every regard except for an active visa.

A significant portion of "illegal" immigration is folks who have overstayed a legitimate work visa (and hence obtained a social security number during the visa application process), and there's also the whole bucket of folks who applied for a social security card under the DACA (which protections have since been mostly rescinded).