She left, returning a few hours later critically ill.
"The circumstances of the patient leaving the hospital are being urgently investigated. We acknowledge this is an extremely stressful time for the family and we have instigated an immediate investigation into the case and circumstances," it said.
The DHB said the hospital was under extreme pressure with high numbers of patients.
Meanwhile, staff health and safety representatives at Palmerston North Hospital's ED had given managers a week to fix overcrowding and excessive workloads there.
The Nurses Organisation said staff had been warning for months that lives were at risk.
It said the representatives had issued three provisional improvement notices covering an overcrowded noisy work environment; lack of staffing resources resulting in untenable workloads; and staff wellbeing and stress, resulting in increased sick leave, burnout and resignations.
One of the representatives, Kirsten Caves, said conditions in the ED had "broken" some nurses.
"There is huge stress and burnout and large numbers of nurses and healthcare workers resigning as a result of that. It's not just in Palmerston North ED but across the country in healthcare we're looking at a healthcare system that is understaffed and overworked," she said.
Caves said cancelling some outpatient clinics and elective surgeries and reducing visitor numbers would help ease the pressure.
Nurses Organisation president Anne Daniels doubted the death at Middlemore would have been the first of its kind.
"I honestly don't believe that this is probably the first time, it's just the first time that it's been found," Daniels told Morning Report.
"My heart absolutely sank because we have been warning that because of the shortages, because of the extreme nature of the high workloads, that something would get missed and that would impact on the health and wellbeing of our patients.
Provisional improvement notices had been put in to several hospitals and these obliged managers find ways to fix issues like staffing, Daniels said. However with the inability to recruit - because there were no nurses to recruit - that was an impossible situation.
In the short term, work had to be prioritised so "life and limb" emergencies were dealt with immediately.
"Unfortunately, that means the urgent takes over the important.
"We have to have the resources to do that and that has to come from somewhere, which means that planned care has to be put on hold.
There had been warnings since 2006 of an extreme lack of nurses by 2021 and successive governments had failed to plan and prevent this, she said.
The Australasian College for Emergency Medicine said emergency departments and health systems across Aotearoa were under extreme and unprecedented pressures.
It said the government's Budget last month failed to tackle areas that contributed to overcrowding and crippling wait times in emergency departments.
"Extended delays in acute care can lead to poorer clinical outcomes which can, at times, include death," the college said.
- RNZ