I'm always amazed at how current the Social Security Death Index is sometimes. My great-aunt died on 1 November of this year (Mildred Trautvetter, there's only 1 in the index) and I noticed that today she is listed in the SSDI at GenealogyBank.
Copies of the SS5 form, the application for a Social Security Number are available from the Social Security Administration.
The image on this post is the SS5 card for my wife's grandmother who died in the 1980s. It is representative of information contained in the SS5 card.
Copies of the SS5 forms for deceased individuals can be ordered from the Social Security Administration via their website.
You should search the SSDI first to obtain name, death date, social security number, etc.