You and your employer face multiple potential problems, some legal legal and some tax issues:
You and potentially your employer may be accused of conspiring to commit unemployment fraud. States know how to identify this. People have been trying to do this for years. Even if a 1009 or W-2 don't show dates, the state may ask for additional information.
They gave you a 1099. It is possible that you were not an independent contractor. The state and the federal government don't like when this happens. They may also go after your employer for this.
You could face tax issues. If the 1099 income was significant enough you may have been required to file quarterly tax forms because of the lack of withholding. The need to file wasn't changed by the fact that you though there wasn't going to be 1099 evidence.
Did you account for your legal income, this income you didn't report, and the unemployment income from the state when setting aside money to pay your taxes? Many people forget that unemployment income is still taxable income.
You know why they sent you the 1099? They couldn't claim your income as an expense once it exceed $600. To claim it they had to tell the government where it went.
All states are required to assess a penalty of not less than 15% of the amount of the fraudulent payment. Other penalties under state unemployment insurance laws generally include criminal prosecution with fines and/or incarceration; required repayment of fraudulently collected benefits; forfeiting future income tax refunds; and/or permanent loss of eligibility for unemployment compensation.
You face choices:
Hope nobody notices
Report yourself and your employer
With your employer, jointly report the incorrect payments and offer restitution. (this is the gold standard).
While self reporting does not change the potential penalties, it speaks favorably of your intent, and has a good chance of reducing the overall cost of the events.