After you die, your Social Security number is removed from active use and placed into the Social Security Administration's Death Master File database. The database catalogues all deaths reported to the SSA. All reported numbers can be found in the Death Master File or the Social Security Death Index database.
Social Security numbers are not reused or reissued after a person dies. The Social Security Administration states that it has enough unused and unregistered nine-digit Social Security number combinations to last for several future generations. The Social Security Administration assigns an estimated 5.5 million new Social Security numbers each year.