The debtor of the wage tax is the employee. However, the employer is responsible for the proper withholding and payment of the wage tax to the tax office. If the tax office discovers during an audit that too little wage tax has been withheld, it can claim the employer or directly the employee for the shortfall.
Every domestic employer is subject to the obligation to levy and pay wage tax. Wage tax must be withheld not only from employees who have a domicile or habitual residence in Germany (employees subject to unlimited income tax), but also from employees who have neither a domicile nor a habitual residence in Germany, but who receive wages from a domestic employer (employees subject to limited income tax).