"Your Social Security numbers are...?"
"Sorry, if you don't have a Social Security number, we can't introduce jobs to you."
...
"If you want to work at a factory, you also need a Social Security card number. The factory checks your past credit record, and according to the laws of Dawn City, all employers must purchase social insurance for their employees."
"Is there any work that doesn't require a Social Security card number? I don't know about that. We are a legitimate job introduction agency. You can ask at other places, sorry."
...
"Sorry... If you don't have a Social Security card number, the employer can't confirm the employee's identity. If there were any issues, our job introduction agency would also be held responsible. You could try asking elsewhere."
...
They asked several large job introduction agencies in a row and basically received polite rejections.