The couple fled by boat to Uganda, where Mrs Salama gave birth on the run in the open air.
Eventually they found a United Nations refugee camp where they slept under a tarpaulin. They had two more children in the snake-infested camp before New Zealand gave them refuge in 2008.
Everyone else in their extended families was dead.
Public health nurse Allie Fyfe has become their guardian angel. Called in for their health problems, she quickly found they needed wider social support.
Mr Salama was found to have renal cancer almost as soon as he arrived here, and has had a long-term jaw problem which has prevented him from eating anything except soft food since he was 20. He will finally get reconstructive jaw surgery next month.
Mrs Salama has chronic pain from her machete wounds.
But Ms Fyfe also found the family did not have enough warm clothes, shoes or bedding and two boys were sharing a single bed. The children could not afford school activities.
She applied to the children's charity Variety, which offers $35 a month for school-aged children in need.
Two weeks ago the Salamas used their first instalment to buy warm clothes, shoes, blankets, pillows and school uniforms, and pay the children's schools $50 each in advance for the next activity fees.
They plan to get bunks for the boys after the next instalment.
Kiwi kid sponsorship
*Donor pays $35 a month to support a needy child in NZ.
*Variety pays money direct to suppliers for child's needs.
*Donor and child write to each other but do not meet.
*1000 Kiwi kids now being sponsored.
*100 needy children on waiting list.
On the web
www.variety.org.nz