DeWitt, this may be the woman you asked about, in the Social Security Death Index:
VONA E MORGAN, 29 Sep 1927 - 15 Jul 1992. SSN: 439-52-0012, issued: Louisiana.
There are quite a few things you can do with this information. First of all, you can find it yourself at http://ssdi.rootsweb.com
, and attach a Postem to her record. This will help cousin/researchers find you.
Second, you can click on the SS-5 link, to generate and print out a letter you send to the SSA requesting her SSN Application. Information about her parents will be on that application, along with her signature!
Third, you can now search for obituaries for her, which will probably add to the information you know have. Most importantly, it will give you the name of the funeral home, which will hold still more records.
I hope this is helpful,