Your household employee (nanny, housekeeper, maid, etc.) contributes to or pays:
The employer is solely responsible for the remittance of the Social Security and Medicare taxes. Should the employer fail to collect this tax from the employee via periodic payroll deductions, the employer remains responsible to remit or pay the tax to the IRS. The household employee CANNOT remit their share of Social Security and Medicare tax independent of the employer. There is no statue of limitation on the employer's nanny payroll tax obligations.
This is an important point families need to understand! Should the employment relationship end badly or suddenly, the nanny may need to file for unemployment compensation or benefits. In a situation where the nanny was being paid off the books, she will still be entitled to benefits - the only consideration she is likely to have when her groceries or rent are on the line. The family in these situations becomes 100% responsible for all Social Security and Medicare taxes - both the employer and employee portion. There can be substantial back nanny tax payments and unemployment insurance payments, as well as penalties and interest due. The protections of unemployment insurance are extended to all workers, whether they have legal work authorization or are undocumented workers.