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Well she can and should pay the balance of the fine and get the DUI issue finalized. Whatever the warrant issue, the DUI disposition will not be affected. Actually, the fact that she has done everything she is supposed to on the DUI MIGHT work in her favor, despite the fact that she got the dui to begin with.
Regarding the ramifications of the warrant, it totally depends on what the underlying crime was that was the basis for the warrant; whether she had been given mutiple opportunities to appear at the time and failed to do so; the validity of the underlying charge; whether it can be proven; how long ago it was; whether it is a CA or out of state warrant, etc. Of course, failing to appear is IN ITSELF a charge separate from the underlying charge. I would need to know the details mentioned above before I gave you an intelligent answer on that part of the question.
I thought the warrant had to do with an old unrelated case. When was she supposed to pay the balance of the fine? How late is it? Had the judge told her at sentencing that if she couldn't pay on time she must appear and ask for an extension? Did she understand that? How old is she?
Based on her age; the fact she did make regular payments; that she was laid off; and that she is prepared to make the final payment, from my 30+ years experience, unless the judge is really hard, I don't think she will be given jail time. Just make sure she is extremely humble and apologetic when she appears in court and tells the judge she was afraid to ask for another extension after she was laid off and was trying to be independent and not ask her parents for the money.