From the above I see you mentioned California.
There are number of statutes and related crimes associated with welfare fraud including: theft, larceny, obtaining money by false pretenses, federal code and the State welfare act in Califiornia that you could be prosecuted under.
However, there is reason for you to be more hopeful if you are agreeing to pay back the money and being truthful with the investigating officer lesser penalties are imposed.
More likely would be (1) a complete dismissal of the charges
(2) probation or deferred ajudication
(3) tried for a misdemeanor crime rather than a felony or accepted guilt plea for a misdemeanor
As the matter has not been finalized it would be in your interests to be a compliant as possible with investigators as this would influential should they make the decision to prosecute or not to prosecute.
In most circumstances and the way you have described your dealing so far most likely you will be able to get a lesser charge. The meeting will be crucial for this, so best of luck in the meeting.
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