"There has never been any doubt in our mind that Victoria Police are responsible for our mum’s death. The Coroner found that the police should have sought medical care rather than taking her to a cell," the Day family said in a statement.
"The Coroner found that once mum was in the cell, the police failed to properly check on her, treated her with complacency and breached her human rights to humane treatment and dignity."
Ms Day was a 55-year-old Yorta Yorta grandmother. She was on her way to visit her youngest daughter in December 2017, when she was arrested at Castlemaine Train Station for public drunkenness after falling asleep on the train.
Once in police custody, CCTV footage shows Ms Day staggering around the cell and hitting her head several times.
She was later found to have suffered from a bleed in her left temporal and frontal lobes of her brain and died in hospital from her injuries.
The family was saddened to hear that Ms Day's death would have been preventable had the laws of public drunkenness been changed as per the recommendation of the Royal Commission into Aboriginal Deaths in Custody decades ago.
"It is heartbreaking for us to hear that our mum’s death was preventable had she not been arrested and taken into police custody," the Day family said.
"In other words, if the Victorian Government had done what the Royal Commission into Aboriginal Deaths in Custody recommended 30 years ago and abolished the offence of public drunkenness, our mum would still be alive today.
"While it is commendable that the Andrews Government has committed to repealing the offence of public drunkenness - this can not happen soon enough. There can be no reason for delay."
Coroner English also made the recommendation that Victoria Police do not investigate their own officers when it comes to Aboriginal deaths in custody, and that the V/Line train their staff on unconscious bias.
"We are pleased that the Coroner has understood why it is so important that police do not investigate police when it comes to Aboriginal deaths in custody. "There must be independent investigations of police wrongdoing if there is to be truth and accountability," the Day family said.
Coroner English requested that both Victoria Police and V/Line engage the Victorian Equal Opportunity and Human Rights Commission to conduct a review of their training materials provided to employees with the human rights set out in the Charter of Human Rights and Responsibilities Act 2006.
She also recommended that the Department of Justice and Community Safety review the current volunteer model of the Aboriginal Community Justice Panel for its effectiveness in providing protection to Aboriginal people in custody.
"We have lost our mother in the cruelest of circumstances. Our family will never be the same. While there are sparks of justice in today’s decision, this country has so much further to travel," the Day family said.
"For as long as Aboriginal people are targeted by police, are locked up and mistreated, and continue to die in police custody, the fight for true and complete justice for our people will be ongoing."