An inquest into a woman's brutal murder has heard the police family violence section at the Elizabeth station in northern Adelaide was under-staffed and overworked when the woman and her children earlier sought police help.

Lawyer Morry Bailes for the Police Association told the inquest two officers described the workload as "extreme" and "mission impossible".

Senior Constable Kerry Coleman, who used to manage staff in the section, agreed.

She said when Zahra Abrahimzadeh sought police help in early 2009 the section had vacancies.

"There were times [when it was] very busy," she said.

Mr Bailes asked: "There were times when the volume of work could not be adequately performed by the number of members ... do you agree with that?"

She responded: "I do agree with that."

Mr Bailes also said one of the officers told of "a time when there were 55 high-risk matters in the section. Do you recall that time?"

"Possibly, there would be times," Senior Constable Coleman said.

The constable told the inquest the unit had six members but "double would be great, realistically".

She said experienced members had left the section because of the workload.

"There's a brain drain, as it were?� Mr Bailes asked.

"Definitely," the senior constable replied, saying it was hard to fill positions in the section because the job was not the most desirable.

The court heard Senior Constable Coleman was in the supervisory role without any particular training to handle domestic violence.

She conceded she could have done more to follow up the Abrahimzadeh case and the court was told she had faced disciplinary action over her role.

A year after seeking police help about domestic violence, Mrs Abrahimzadeh was stabbed to death by her estranged husband Ziaollah at a crowded function at the Adelaide Entertainment Centre.

The offender is now in jail.

The coroner was told in earlier evidence that a domestic violence worker had advised police Mrs Abrahimzadeh was "petrified that she's going to be killed".