That arrangement sounds highly irregular. I hope that you will consult with a lawyer before entering into any agreement with your employer. At the very least

That arrangement sounds highly irregular. I hope that you will consult with a lawyer before entering into any agreement with your employer. At the very least it seems like they should have recorded your employment for tax purposes. Even if you aren't obliged to pay any taxes to the US government, there must be some bare minimum for accounting purposes and internal audit controls. Of course, I am neither a lawyer nor experienced in administrating the employment of foreign nationals