Legal Question in Immigration Law in New York

Technically, yes, an undocumented resident of the US can own a company. Legally, that individual is not authorized to work in the US, so he/she should have employees who are work authorized running the business and then the undocumented resident as the owner may be permitted to benefit from profit taking. If the immigrant is deported, as a practical matter the company will only continue on if that person has put management in place to run the company in his/her absence. The company would not simply legally dissolve if the owner is deported.