I'm not a tax accountant, but as a self employed person, I have to play tax accountant 4 to 6 times a year. You have to file and pay your taxes every year. Your mom will have to pay penalties on what she owes. If the amounts are small, it's likely that the IRS isn't bothering with coming for whats owed, but they can. Or in this case, NY State dept of taxation instead of the IRS.

Personal income tax is your personal income tax. Withholding is a form of prepayment. It doesn't change your total tax burden, and it isn't a tax on your employer, its on you. Your employer pays separate payroll taxes that you won't even see.