If it was mailed long ago, it's probably lost in the mail so ask them to issue a replacement which should arrive in 2-3 weeks.
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If the social security was sent and lost in the mail, ask Social Security to issue you a new one and flag the old one.
I'd be shocked if SSA ever issued a different SSN for someone.
They have done it, but only in rare circumstances like Witness Protection Program or extreme cases of identity theft.