Forms are not required from an employer in order to pay taxes on income. The nanny would simply report the amount of cash received as her taxable income which she is supposed to do under the U.S. Tax laws. The employer, if audited, would be penalized for failure to report the wages actually paid to an employee.
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Yes, she can and should file her returns based on her records of what she received. This could possibly mean an investigation of you and why you did not file information returns, but the chances are extremely unlikely.
This is not intended to be legal advice, and is general in nature.
As otherwise addressed she was free to report what she earned. If you hit audit, get a tax controversy lawyer or enrolled agent on the case as quickly as possible.
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