Tax-wise, it makes no difference what the taxpayer's legal immigration status is and the tax law applies equally to all, whether the income is legally or illegally acquired, reported or unreported by the payor.

As you may already know also, US tax status is determined by §7701 which, in turn, determines the tax regime the individual falls under.

Technically, you could consider various tax positions as you would with other taxpayers.  Yours, however, sounds more like a legal question that should be raised to an attorney.