Social Security Applications may have been filed any time after Social Security started. SS# are needed now for bank accounts. My Great-Grandmother applied for a SS# in 1966, for a bank account. Someone who died in 1966 may or may not be listed in the SSDI. I have at least one cousin who died recently and is not listed in the SSDI, heard that he will not be listed there because he was on Social Security Disability.