They say their family has strong attachments to the property. Bodies of loved ones have been held there before tangi, including a cousin Mairina Dunn, 17, murdered by Nathan Fenton in 2007; children have been born there and afterbirths buried in the grounds.
The Dunns also say they have nowhere else to go.
But Housing NZ said the men have had plenty of time to organise other accommodation.
Northland tenancy services manager Angela Pearce told the Northern Advocate that at two meetings, on April 2 and on May 11, the family was told changes made last year to the Residential Tenancies Act clearly stated that when an agreement-holding occupant dies the tenancy automatically ends.
Ms Pearce said the brothers were advised to test their eligibility and apply in their own right for another state house. HNZC could also help if they qualified for urgent interim housing, she said.
The men have not taken those steps. They say it is a waste of time and administrative resources for them to be forced out of one state house into another.
"This is a case of the state kicking people out of the home they grew up in ... but it's not just about my brother and me, the state is kicking little kids onto the street with no guarantee they will help us find another place to live," Raymond Dunn said.
"In a few days the state would have made us homeless. All we're trying to do, at the end of the day, is keep our family home."
He said at one meeting a senior HNZC staff member said that "if you are a Dunn or associated to a Dunn you will never get this particular property".
The staff member has denied saying that but an independent advocate working with the family told the Northern Advocate she was also there and heard the comment.
The Dunns also claim they have been wrongly labelled and discriminated against by HNZC staff for being gang members, but Ms Pearce said the housing authority does not take gang affiliations into account when assessing eligibility.
Whangarei MP Phil Heatley said he could not comment because of a conflict in him being the Housing Minister and local MP. Mr Heatley said he approved of the tenancy policy changes that prevented inherited tenancy, without exception.
Te Tai Tokerau MP Hone Harawira supports the Dunn family's request to stay in the house. Mr Harawira said he saw no reason why HNZC's policy to stop inherited tenancy could not be flexible.
Meetings between Mr Harawira, the Dunns, their advocates and HNZC staff have been postponed but failed to win a stay of execution on the family's eviction. Time has run out but the Dunns say they will not move.
HNZC has said that if they are still in the house at midday on Monday, legal action will be taken to enforce the eviction notice.