You don't need to be a citizen to get an SSN. There's also tons of scenarios where you can end up undocumented after obtaining an SSN.

Common scenario: USCIS granted you a SSN, but aren't done processing your Asylum status (see - https://secure.ssa.gov/poms.nsf/lnx/0110211205 , https://assets.aila.org/files/21f06205-c2ce-4512-860c-f98dfc60d0cb/19091330.pdf?1697590715).

Another common scenario: visa expired (see - https://www.ssa.gov/number-card/request-number-first-time).