Herron, 25, had struggled with heroin addiction and had been rough sleeping and couch surfing

As family and friends of Courtney Herron come to grips with her death, Victorian authorities are grappling with how homeless people with drug addictions and mental illness are falling through cracks in the system.

Herron’s family on Monday visited Royal Park, in the inner Melbourne suburb of Parkville, where her body was found by dog walkers on Saturday morning.

“We are heartbroken by the loss of our daughter,” the family said in a statement. “Courtney has a family who love and care about her. The loss has devastated our entire family.”

The 25-year-old former private school student had struggled with heroin addiction and had been rough sleeping and couch surfing.

Herron’s friend Jessica Bateman said the system had failed her.

“She was trying to get into public housing, she was trying to get on to methadone or something that would stop the withdrawal symptoms that she was going to face – and the fear of withdrawal is what really kept her using,” Bateman told Network Ten.

Guardian Australia understands about 10% of the 14,500 Victorians on the state’s methadone program are homeless.

People need to be on the program for three months before they are eligible for takeaway does of methadone. Storing the dosages safely could be an issue for homeless people because the medication could be stolen and has a high value on the the black market.

The Victorian Alcohol and Drug Association’s executive officer, Sam Biondo, said some people have trouble accessing a methadone prescriber or dispenser particularly outside of the Melbourne metropolitan area.

A $5 dispensing fee, which sometimes needs to be paid upfront a week in advance, can prove a barrier for some people with addictions.

The Launch Housing chief executive, Bevan Warner, lamented hundreds of Victorians are being turned away each week because of a shortage of crisis accommodation.

“There are 423 funded crisis accommodation beds in Melbourne and there’s close to 2,000 people sleeping rough,” Warner said. “It’s very hard for someone to recover from an episode of mental ill health ... or to deal with a substance dependency issue if they’re spending most of their waking hours worrying about where they are going to sleep tonight and if they’ll be safe and secure.”

Victoria’s Council to Homeless Persons says there are 82,500 people, including almost 25,000 children, on the public housing waiting list and a shortfall of 102,800 properties.

The council’s CEO, Jenny Smith, said the state government needed to be delivering 3,000 social housing properties a year to make a dent. But the Victorian government’s budget, which was handed down on Monday fell well short. It committed $209m towards building 1,000 new public housing units by 2022.

The Victorian premier, Daniel Andrews, defended the size of that commitment.

“That’s the number we committed to at the election last year,” Andrews told ABC Radio on Tuesday. “We will do what we can do. We will build the housing units we can afford to build.”

He noted the inadequate mental health system had also been topical in recent days and he hoped the state’s royal commission would help fix the problems.

Homeless man Henry Richard Hammond, 27, faced court charged with Herron’s murder on Monday.

His lawyer said Hammond had mental health issues and the case will return to court in September.

Herron and her alleged killer may have left a party together just hours before her death, according to media reports.