Couple of additional points. If your girlfriend is working in the US, she owes US income tax (either as a non-resident or resident, depending on the substantial presence test). She can (and legally is required to) file a tax return and pay US tax on this income even if it is paid in cash. The IRS keeps tax returns confidential and will not inform on her to Immigration authorities that she is working without proper authorization.
Additionally, if she does apply for citizenship, one of the application questions is "have you paid all US income taxes that you might have been required to pay?"
