She was living in a cave on Sydney's leafy north shore when she died, her few possessions scattered about her - a pillow, a blanket, three plastic containers.
Residents of the affluent harbour suburb of Middle Cove knew her face - she was often seen walking nearby streets - but no one knew her name.
Now police are hoping someone will put the two together.
"She's obviously the daughter of someone," the officer in charge of the case, Constable Andrew Schepis, said.
"Perhaps there were some family issues that caused them to become disconnected - we're unsure,"
A passer-by stumbled on the woman's body in February, in an area of dense bushland in Willis Park. Police believe she died as a consequence of being homeless.
Witnesses told police the woman had been living in the cave for six or seven years.
"She was well-known to residents as she routinely walked Eastern Valley Way," Schepis said.
"We've checked out most homeless refuges, she's not known to them - which to us is very odd,"
She also has no record with police and is unknown to the Registry of Births, Deaths and Marriages.
Schepis said that after extensive inquiries, including forensic tests, police had been unable to identify her.
They believe she also lived in Queensland at some point.
The woman gave Queensland police the name Jemima Ann King in 2002 but investigators have since confirmed that was not her real identity.
The results of an autopsy are incomplete but her death is not being treated as suspicious.
- Sydney Morning Herald