The Social Security Act regulations have specific rules regarding social security numbers (“SSNs”). See, specifically § 422.103. Social security numbers.
These regulations, specifically explain a number of rules regarding applying for a SSN, obtaining a replacement social security card (with 10 maximum lifetime replacement cards), how SSNs are assigned, and how the Department of Homeland Security can have an agreement with the Social Security Administration regarding issuance of SSNs for those who have immigrated to the U.S. – See, for instance § 422.103(b)(3) 
- (3) Immigration form. SSA may enter into an agreement with the Department of State (DOS) and the Department of Homeland Security to assist SSA by collecting enumeration data as part of the immigration process. Where an agreement is in effect, an alien need not complete a Form SS-5 with SSA and may request, through DOS or Department of Homeland Security, as part of the immigration process, that SSA assign a social security number and issue a social security number card to him/her. Requests for SSNs to be assigned via this process will be made on forms provided by DOS and Department of Homeland Security.
Applications for a SSN are completed through a specific Form S-5, located on the SSA’s website. This Form S-5 discusses the general requirements for a SSN as set forth in the law; i.e., the individual must be either (1) a U.S. citizen, (2) have lawful work authorized immigration status, or a (3) valid non-work reason for requesting a SSN and a card.
Interestingly, there appears to be no statutory or regulatory rule in the law that allows an individual to somehow “expunge” or otherwise terminate their SSN, once obtained, even after loss of USC or LPR status.