I have a question about an insurance lapse issue?

My vehicle is insured in NY and I have a concern becuz my mom's insurance had lapsed as of the 26th of this month and the insurance is trying to work things out with her by having her pay half for now (the whole bill is $185). I took my name off and got my own coverage, so Ithought it was gonna be cheaper. My question is if she pays the penalty amount which is $8 per day within 1-30 days, will they reinstate or keep her insurance going? Also, does these penalties apply in every state?