Yes, a foreign company could do that. But if they have an employee working in the U.S., the company becomes a U.S. employer. They have to follow all the U.S. laws that apply to employers, including withholding taxes from the U.S. employee's pay and issuing a W-2 at the end of the year. They also have to follow the state laws for the state that the employee works in, including withholding state taxes. Most foreign companies would not want to deal with all this red tape for just one U.S. employee.
