The trio were found collapsed in their home early Saturday morning after becoming violently ill hours after eating their evening meal. The couple's two young children shared the same meal but did not eat the wild pork.
Friends visiting in hospital say they are now largely unresponsive and in a vegetative state with only brief spells of consciousness.
Doctors are understood to be puzzled at the dire impact of the suspected poisoning. Meat from the boar, which was shot by Kochummen on a hunting trip, has been taken away for test.
Findings from a detailed toxicology report are expected today.
Speculation is mounting the suspected food poisoning is a rare case of botulism. Others have suggested the family may have been poisoned by 1080 which the wild pig may have eaten.
Neighbours and members of their Hamilton Anglican church congregation have rallied around the stricken family taking care of the couple's young children and liaising with health, embassy and welfare authorities.
Today Joji Varghese said family from the southern Indian state of Kerala were now heading to New Zealand to be at their bedside.
"We are expecting the extended family to arrive in the next few days. Their visa processes are under way," he said.
A public health investigation is under way.
Yesterday the region's medical officer of health said there was no wider public threat but urged people to follow safety guidelines prepared wild game meat.
"We do not have any evidence to determine any broader contaminated game meat, or that there is a risk to public health, however I would encourage anyone who is hunting or handling game meat to follow guidelines as set out by MPI," said Dr Richard Vipond.
Hunters were today at a lost to explain how eating wild boar meat could have caused the family to fall so ill.
Hunter Alan Simmons said he was as confused as most other people.
"If the animal hasn't been handled very well and it's gone off you'd soon know about it - you wouldn't eat it - your nose would stop you from eating it," he said.
Most poisons he was aware of would end up in the animal's gut cavity rather than the muscle tissue.
He even wondered if a dead pig had been harvested that had died after being poisoned.
The NZ Deerstalkers' Association president Bill O'Leary told the Herald he had never heard of anyone being poisoned from game meat - but it was not that uncommon for wild animals to be dropped off at a game butcher and then be deemed unfit for human consumption.
"From a hunter's point of view, this is the first incident I've heard of a number of people going down," he said.
O'Leary questioned how the meat was treated, including whether it was gutted quickly and safely and how long it had been left out before or after cooking.
He also said it was important for hunters to get their kill somewhere cool quickly especially as temperatures rise.
