Thanks for the chance to help. I am an attorney with over 12 years experience. Hopefully I can help you with your legal question.
What you describe is a crime. It is a class A misdemeanor
...not as serious as if she had hit a person, or hit a car with another person in it. But it is still a crime.
The crime was complete when she left the scene of the accident. That makes it difficult...since the crime was complete, technically, she is already at risk for prosecution/conviction. If she goes back and reports this, the police can prosecute her for the crime based on her confession.
Of course, if there are cameras that recorded the incident or there are witnesses who can testify to what happened, she could be prosecuted as well.
The good news (if there is any) is that this is a relatively minor incident...even if she takes no action and is arrested, the very worst thing that can happen is a misdemeanor conviction. Not good...certainly, but since there were no injuries it is not a felony. And for a first offense misdemeanor, again, even if she is caught and does not turn herself in, it is highly unlikely she would do any time in jail.
for a period of time and a fine/restitution
to cover the cost to replace the sign.
So she has a choice
She can go to the city/county or the police and report this (if this was a stop sign the city/county will be the ones who have to replace it). I would expect he police to write this up (send it to the city prosecutor to have them file charges) but if she reports this, there is a decent chance they reduce the penalty and perhaps only charge her with an infraction (so no criminal record). There is no guarantee...she is at the mercy of the prosecutor...but what you describe, this is so minor I would expect the city prosecutor to reduce the charges if she comes forward.
Or she can take a chance that it was not seen by anyone....it may be she is never arrested. But if she is arrested, it is unlikely the prosecutor would agree to reduce the charges...they would still offer a plea deal...again, I do not expect jail time...but I would expect them to keep the criminal charge (violation of 625 ILCS 5/11-404) in place
Let me know if you have more questions...happy to assist if I can