She needs an immigration lawyer.
Just to be pedantic, you don't technically need to be a citizen or perm res OR have a visa to be in the us legally, in some cases. Canadians and mexicans can come in on a TN status. It's commonly called a TN visa, but technically it is not one, and they can stay in the US and work.
In regards to her chances now, as sad as some may think it is, if you're married to a US citizen the bureau of citizenship and immigration is notoriously dismissive of any "overstays" or "out of status" situations. Basically they often just don't care. They're quite forgiving, which is why you'll rarely hear of somebody getting booted out of the country while their us citizen spouse is still in the US.
Of course, my original point stands: she needs an immigration lawyer.
Why she hasn't gotten a greencard is beyond me. When you marry a US citizen you can fast track to get one. It's quite cheap and the application is fairly easy to fill out, or costs little to bring such a simple case to an attorney.
If they were going to deny her USC they would have told her. Maybe they did, but she didn't get the mail or something.
I'd be surprised if she's deported. The US has 10 million illegal mexicans in its borders right now, most of whom are not married to USCs, and there is hardly any effort to deport them. Basically US immigration is in such a screwed up state right now that she'll probably just end up having problems like not being able to get an SSN as opposed to expecting the gov't to pay for a one way ticket to Korea.