If the state assesses a penalty, that's between the employer and the state. No, you don't see any of that money.
However, you are allowed to bring your own suit to which you may recover up to $4000 plus legal fees.
But before you do any of that, as Zig says, did you ask why you aren't getting the stubs. Employers are allowed to instead use an electronic statement (ONLINE web site or the like) rather than paper stubs. Your chances of prevailing on a lawsuit are pretty limited to people who are likely not only not providing stubs but just paying out of a general account rather than doing the full employee thing (including tax withholding, payments for UI, etc...).