Brandon Yates, 28, was fatally wounded on August 17 but authorities are yet to make any arrests over the incident in Wollongong, south of Sydney.
Investigating officers were told Mr Yates left a unit on Crown Street, returning a short time later with a stab wound and eventually collapsing.
Paramedics treated him but he never recovered and his family turned off his life support in hospital six days later.
Mr Yates' nan Rossilynne described him as the sort of person who would "basically give you the shirt off his back", pleading with anyone who knows what happened to talk to police.
"We just want someone to come forward and give us closure, at least," she said.
"It all seems so senseless."
Shantelle Yates, Brandon's sister, said he was the "cheekiest, most mischievous person" and opened up on the emotional experience of seeing him in the emergency department.
"(It was) totally devastating, waking up and getting that phone call, getting to the hospital, just seeing him pretty much gone in a coma, knowing that someone would take my brother's life for nothing," she said.
"Switching off his life support, having to watch my brother pass away, because someone wanted to take his life, I now have to pay the consequence of losing my brother, losing my best mate."
Police also released CCTV footage of a man they believe could help with their investigation.
The vision showed a man wearing dark clothing riding a bicycle past a nearby school around the time of the stabbing.
Anyone with information surrounding the incident has been asked to contact Wollongong police or Crime Stoppers.
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