The Employment Insurance system was created as a way to support workers should they find themselves without a job, as well as to assist them financially as they search for new employment.
All employers are obliged to enrol their employees in this system. This insurance system is also available to foreign workers who are in possession of visas that carry no restrictions on their professional activities in Japan, unless you are employed outside of Japan or draw unemployment benefit from another country.
For more details you can consult Hello Work or the local Public Employment Security Office.