Police Scotland said that apart from her carers, the last independent sighting of Margaret Fleming was on 17 December 1999 at a family gathering.
The 36-year-old was reported missing by her two carers from her home in Inverkip at about 17:40 on 28 October.
Officers want to hear from anyone who knew Ms Fleming from her college days.
Ms Fleming, who is believed to have learning difficulties, is thought to have attended James Watt College in Greenock between 1996 and 1998.
An on-going search of her house in Main Road will now extend into the garden, which police say will be extensive and will involve some excavation work.
Det Ch Insp Paul Livingstone said they had found no trace of a job, few friends, and no evidence of her contact with partner agencies and local services.
“One line of inquiry that I now must consider is the possibility that Margaret may have come to some harm,” he said
“Our search will continue from the house into the grounds around it.
“This is a natural progression in the inquiry to assist our investigation to find Margaret.”
However, he stressed it was still a missing person investigation.
“Margaret’s carers have said that they believe she has a private side to her life and that she may have friends that they are not aware of,” he said.
Ms Fleming is described as about 5ft 5in tall, with collar-length black hair, brown eyes and has a heavy build.
When last seen, she was wearing a green tartan fleece or jumper, dark jeans or trousers, and dark Karrimor-type boots. She also had a satchel-type handbag.
It is believed Ms Fleming lived with her father in Port Glasgow before he died in October 1995.
She then lived with her grandparents and mother but moved in with carers in 1997, and has been estranged from her mother since then.
Officers from the Major Investigations Team are now assisting police at Greenock with the investigation.