Unclaimed or indigent people in Los Angeles County are generally sent to the Los Angeles County Crematory Cemetery
(read the detailed info on the link). Many cemeteries (and organizations) also have plots set aside for those who don't have resources.
Hopefully, she would have a death certificate that would be on file at the L.A. County Recorder's Office, and you could order a copy. That would confirm where she was buried.
You can check the California Death Index (1940-1997)
or, if she died prior to 1940, there are some of us with access to other indexes that would be glad to take a look. Just post what you know about names/dates/locations.