The National Archives has a wealth of information you can use in researching your family. One thing you can find there is Social Security Records. There you will see social security applications and social security death files. These documents are for the years 1936-2007 and for people who have a verified death date or who would be 110 years old by December 31, 2007.
Click on the search button for the group that contains your last name. You do not have to fill out all the spaces on this form. In fact, it may be good to leave a few blank, i.e., my mother always told me she was born in Stuttgart, but her social security application says she was born in Almyra. If your search turns up a record, you can see their social security number, citizenship, full name, date of birth, race, ethnicity, sex, mother’s full name, father’s full name, city of birth, for women you can see if they received a duplicate card due to a marriage and the previous marriage name.
Scroll down to the death files and look for your ancestor there. You can find their social security number, full name, date of birth, date of death, sex, and zip code of residence.
Another good resource for searching the Social Security Death Index is the website of Stephen P. Morse. These are records between 1936 and February 28, 2014. His article “Decoding Social Security Numbers” can be a good resource for clues about your ancestors.
Good luck in your research.