Miss Foster's family and friends have turned to the internet in an outpouring of grief to share their stories of a mother who was taken before her time.
A Givealittle page was set up by Renee-Lee Hunt, who said Miss Foster was a strong, bright, caring, beautiful, fun person.
"She worked so hard to provide the best life she could for her and her daughter and all of her dreams were finally coming true, her hard work was paying off," she said on the page.
"Unfortunately she was taken from us too soon so we would like to begin a givealittle with all funds raised going to her daughter who not only lost her mum but her best friend. All donations will go directly in to a not-for-profit bank account set up in [Miss Foster's daughter's] name to help her family provide for her and also to help with funeral costs if they need."
Miss Foster's employer Plunket also expressed how saddened and shocked they were at the "sudden death" of the Napier nurse. "Victoria was a valued and respected part of our team, and the kind of Plunket nurse that makes our support for families and children so appreciated by the community," Plunket chief operations officer Andrea McLeod said.
"Her death is a huge loss for our organisation and we are supporting Plunket staff through this difficult time. Our thoughts are with her family for their loss."
Miss Foster was found dead at her Westshore home by police around 9pm on Monday.
A post mortem was held yesterday in Palmerston North.
Eastern District police communications manager Kris McGehan said police were likely to receive a report on the autopsy, "tomorrow at the earliest".
According to police, the man was shot by officers in Clive following a pursuit after the death of Miss Foster at her Westshore house. He remains in hospital in a stable condition.
The man is alleged to have fired three shots from his vehicle during the pursuit.
He was stopped by police on Main Rd, Clive.
Detective Inspector Mike Foster urged anyone who saw a man driving through Napier and Hastings on Monday night in a red 1996 Toyota Corolla 1.6 saloon to contact police.
Police were keen to speak to anyone who may have seen the man driving between Westshore, Tamatea and the Hastings suburb of Raureka between 8.30pm to 9.30pm. It is not known what specific route he took.
Police began a pursuit of the car in central Hastings around 9.45pm, which continued on to Karamu Rd and State Highway 2 towards Clive.
Mr Foster said there were many questions still unanswered.
"We are very much in the early phases of our inquiry and there is a lot of work ahead of us. We're unable to talk in detail about the circumstances surrounding the incident, what took place, or any interactions between police and the man, as this could compromise our investigations," he said.
As well as a police internal investigation, the Independent Police Conduct Authority is investigating police practice and procedures.