You can get a replacement card for free if your existing card has been lost or stolen. You may not need a replacement, as it's your Social Security number that is important and if you know this number, you won't need a replacement
What do I do in the instance that I do not have permission to work but I need a Social Security number for other purposes?
I will refer you to the "If you do not have permission to work" section on the website
What are the options if I don't have one of these specific documents that you mentioned?
Do you have the Employee Identification Card?
no
and the school ID card?
yes
then we can verify your identity with the US Passport
What if I have not updated any document with my old name?