According to the State of New Jersey Department of Labor and Workforce Development, an employer is allowed to cut an employee's pay as long as advanced notice is given to the employee. CBS news confirms that this is a federal law and not confined to one state.
The State of New Jersey further explains that there are several conditions imposed on pay cuts. Cuts cannot be retroactive for time the employee has already worked, and the employer cannot bring the employee's total pay rate below minimum wage. According to the Guardian, pay cuts are often offered as an alternative to firing staff.