Employee or former employee — Enter the name of the person. Social Security Number — Enter the Social Security Number of the person.Jobs With Social Security. How to File an Application for Employment. The following is a list of the required and optional documents that companies most commonly include in the new hire packet. Not all forms are listed. It is not illegal for an employer to ask you for your social security number (SSN). HOWEVER you are in no way obligated to provide your SSN. Form I-765 – Application for Employment Authorization. Fill out and sign this agreement: I, (print your name).