To find your ancestor's place and date of death, search here: http://ssdi.rootsweb.com/
You can also send to the Social Security Administration to request a copy of your ancestor's Social Security application.
http://www.ssa.gov/foia/html/foia_guide.htm
Here are some more links to Social Security information:
http://www.socialsecurity.gov/history/ssn/ssncards.html
http://www.ancestry.com/learn/library/article.aspx?article=895
http://www.ancestry.com/search/rectype/vital/ssdi/faq.aspx
http://www.genealogyandhow.com/lib/research/ssdi.htm