Housing New Zealand says it is spending more than $20,000 repairing homes that become vacant, and reducing the likelihood of mould.
Last week, Radio New Zealand told the story of an Auckland woman Te Ao Marama Wensor whose mouldy state home is being partially blamed for severe health problems in her son, Iriah.
This week, she turned down the offer of another home, saying it too was mouldy.
But Housing New Zealand said the house was not ready.
The house itself is in a poor state.
Most of the walls have holes and peeling wallpaper, and all the walls are scribbled on.
The carpets are stained and in the kitchen, in the area where the fridge was, is a mass of dead cockroaches.
John Tubberty, the regional portfolio manager for Housing New Zealand, said some walls were also mouldy.
"It's from a build-up of moisture in the room, no ventilation, and no-one wiping it down.
We get our properties tested quite often, and air tested, and you can get certain types of mould which can be cleaned by the tenant, versus the risky stuff like stachybotrys which you have to get professionally removed."
Mr Tubberty said it was arguable that the dirty marks on curtains, windows, and around walls was mould.
"It could just be dirt and grime from cleaning," he said. "If you don't ventilate, a lot of that dirt on the windows that you see there just would be results of cooking without opening the windows."
He said the average spend to get a recently vacated HNZ house up to standard for the next tenant was $10,000, but this property would probably need $23,000 of work.
Housing New Zealand area manager Scott Foley said housekeeping was a shared responsibility between the agency and the tenants.
"If the mould is quite minor, we'll ask the tenant to clean it up because it is their responsibility at the end of the day to keep the home in a reasonably clean and tidy condition.
"If we identify that the home has a leak and there's some mould as a result of that, then that's something we need to maintain as a business, so we'll be liaising with our contract team, our maintenance team, to get in as soon as possible and repair that."
Figures from June showed there were 4541 applications on the social housing register - with 49.9 percent of them in Auckland.
Scott Foley said they prepared homes in an average time of 25 days.
"We turn around our vacant houses as quickly as we can. If you think we have 7000 - 8000 vacant homes per annum, if we can shave a day off each of those homes, then we're housing more people in the long run."
Just around the corner from the first house is one that is almost ready.
Gardeners are working at the four-bedroomed house, and the new kitchen is being fitted.
Mr Tubberty said he knew that even when they provided heaters, some tenants could not afford to use them, so to help heat retention and reduce mould build-up, home upgrades were changing.
One change is to install plastic "wet walls" around entire bathrooms.
"We've been doing it for a few years now. It makes it easier for tenants to clean. We've now included the ceilings as well because we know tenants find it hard to clean the ceilings so putting wet wall linings up there, it protects the asset, makes it easier to clean, reduces the incidents of mould."
Mr Tubberty said cooker range hoods and extractor fans are now mandatory, and thermal curtains are in 15,000 homes.
Houses were still inspected at least once a year, and air checks could also be carried out.