No, the Social Security Administration (SSA) does not reuse numbers. It does not reassign a Social Security number (SSN) when the person holding that nine-digit combination dies.
About 454 million SSNs have been used to date. The SSA says it issues about 5.5 million new ones a year but has enough unused numbers to last for “several generations into the future.” That’s in large part because of an overhaul of the numbering system put in place in 2011.
https://www.aarp.org/retirement/social-security/questions-answers/do-identification-numbers-get-reused.html