I don't know that your girlfriend definitely will be prosecuted for fraud. I am only saying that the government has the right to do so, whether she pays back the money or not. The civil statute involves restitution for the monies owed. The penal law punishes the unlawful act.
To be on the safe side, she should retain a lawyer and talk to him in full about what happened before sitting down with the Welfare people. You were the one to have mentioned that she has a meeting "for fraud." I don't know whether that means they have already made a determination that fraud has likely occurred, or whether this meeting is entirely investigative in nature. I do know that she should have a lawyer because she would want to maximize whatever protection the law affords her.
If what she did was indeed a mistake, that would be a defense to a fraud, but it does not mean that she still couldn't be charged and prosecuted. It would just mean that if her defense held, she couldn't be found guilty. The standard for an arrest and a prosecution only requires something called probable cause -- just a reasonable belief that a crime may have been committed
and that a particular person might have committed it
. So if Welfare feels that this may not have been a mistake, they will turn the matter over to the DA's office to see whether or not the DA feels so too. If the DA thinks there's probable cause
to believe she might have committed a fraud, it will press charges.
A conviction, however, is something else again, as a conviction requires proof of guilt beyond a reasonable doubt, And fraud requires the intent to do something dishonest, which you and your girlfriend believe she did not have.