Closing submissions in the Coroners Court case into the disappearance of the pair were heard today following a three-week adjournment.
The coronial hearing in front of Coroner Marcus Elliot aims to establish whether the pair are dead or alive.
Police lawyer Deirdre Elsmore argued the pair died by murder-suicide when Beckenridge drove his vehicle off the cliff in the Catlins in Southland in 2015.
"It's important in this context to consider John Beckenridge's personality, his relative dysfunction prior to the change in custody and the clear change in his personality that was witnessed by a number of witnesses."
Beckenridge and Mike (11) vanished in March, 2015.
His car was found at the bottom of a cliff in the Catlins two months later; however, their bodies have never been found.
Elsmore referred to police conclusions that recovering bodies from this particular coastline was generally difficult.
"Beckenridge planned to ensure that it [the car] landed in the sea, he planned to ensure that the bodies would not be found.
"There's no mystery, and there is a question mark in relation to this matter, as to why they were not found, but that it is not a mystery based on the evidence."
But Mike's family believed there remained unanswered questions. His mother Fiona Lu believed the pair were still alive.
'Dangerous' to conclude pair deceased
The family's private investigator, Mark Templeman, appearing via video link, said police evidence on the case was "insufficient".
"John Beckenridge planned an escape from New Zealand for himself and Mike and this plan included the staging of their suicide at the Catlins.
"I submit that John knew before the Family Court hearing that he was likely to lose custody of Mike and that he and Mike agreed a plan to stage their deaths."
In his submission, Templeman said there were doubts around the pair being in the vehicle when the car drove off the cliff and that police did not seek a "second opinion or independent review" on the evidence found at the crash scene.
Elsmore proposed a further independent review of police evidence be completed.
Templeman said it would be "dangerous" to conclude that the pair were deceased.
"I submit that this investigation should remain open as sightings are still being received that have not been investigated by the police inquiry team.
"Fiona Lu believes that Mike is alive and expects that he will return to her once he is no longer under the influence of John Beckenridge."
A woman who claimed she spotted the pair while holidaying in Indonesia in 2015 provided evidence earlier in the hearing.
Elsmore believed it to be "an honest mistake" and that much of her evidence was unreliable.
Lisa Preston KC provided closing arguments later in the day.
Proceedings have again been adjourned, with the court unable to hear remaining evidence and further submissions today.
Another court date will be scheduled for the coming months.
