That's very unfortunate. There really isn't anything you can do, marriage or not. Marriage to a US citizen, or otherwise becoming an "immediate relative" (the spouse, parent or unmarried minor child of a US citizen) can cure problems of overstaying a visa or working illegally. But it cannot cure illegal entry.
To be sure, there are ways of curing that, but I don't believe any apply in this case. Although it is no longer current law, the old provision known as "245(i)" (a reference to that section of the Immigration and Nationality Act
, or INA) can still help some people, but only if they've been here since at least December 21, 2000. And then, only if there were the beneficiary of some immigrant visa
petition filed on or before April 30, 2001. It doesn't sound like 245(i) applies in her case.
Others who illegaly enter can get green cards
by self-petitioning under the Violence Against Women Act (VAWA), but this requires showing that someone (even a man) is the vicitim of domestic violence or other "extreme cruelty" at the hands of their US citizen or green card holding spouse. As your girlfriend isn't married, it doesn't sound like VAWA is a possibility.
Others file for asylum, but this must be done within 1 year of entry except under extreme situations that are very rare.
I believe that under current immigration
law there is no way to cure your girlfriend's situation. There are over 12 million people in the US in a similar situation with no path to legalization. Everyone agrees, more or less, that something must be done to fix this. It's hard to say when immigration reform will come and who it will benefit, but something will happen, that much is clear. I wish I had better news for you and your girlfriend, but that's unfortunately the current state of the law. I sincerely XXXXX XXXXX when immigration reform comes round it does benefit you both. Good luck.