Social Security records include applications for Social Security Cards and applications for Social Security benefits, among other records. The SSA uses the "120 year rule" for record access when no date of death exists, and a death certificate, obituary, newspaper article, or police report is required to prove death. Parents' names and sometimes places and dates of birth are redacted "unless they are proven deceased, have a birth date more than 120 years ago, or the number holder on the SS-5 is at least 100 years of age." There is a fee associated with requesting SS records; visit the page for current rates. The Legal Genealogist has an excellent post about what to expect during the process of ordering the SS-5.
Request for Deceased Person's Social Security Record
Request for Deceased Person's Social Security Record