Yes. But in Scandinavia, unlike the US, it is a unique identifier and there is a single national database.
"UNIQUENESS. The SSN is not a unique label. More than 4.2 million people, by the Social Security Administration's own estimates, have two or more SSNs. More serious, although much less prevalent, are the instances in which more than one person has been issued or uses the same SSN."
"UNIQUENESS. The SSN is not a unique label. More than 4.2 million people, by the Social Security Administration's own estimates, have two or more SSNs. More serious, although much less prevalent, are the instances in which more than one person has been issued or uses the same SSN."
https://archive.epic.org/privacy/hew1973report/c7.htm