Gov (do not include your Social Security Number in your email message). City of Phoenix employees should not ever have to pay a fee.Not all forms are listed. You are only eligible to apply for a Social Security Number (SSN) if you have on-campus employment or authorization to work off campus. Jobs With Social Security. How to File an Application for Employment. Social Security Number: 8. Most online recruiters only ask for the last four digits of your social security account number. All US employers must properly complete Form I9 for every individual they hire for employment in the United States. This includes citizens and noncitizens.