No. The Social Security Administration does not reassign a Social Security number (SSN) after the number holder's death. Even though the Social Security Administration has issued over 420 million SSNs so far, and the Social Security Administration assigns about 5 and one-half million new numbers a year, the current numbering system will provide enough new numbers for several generations into the future with no changes in the numbering system.

Additional information is available on the Social Security Administration’s web site. See the Social Security Administration’s publication, "Social Security: Your Number," publication number 05-10002.