The Driefontein accident was caused by a seismic event at about 1:30 p.m. local time on Thursday, Sibanye said.
According to NUM spokesman Livhuwani Mammburu: "Before our members go underground we always tell them they are empowered by the Mine Health and Safety Act to refuse to work in unsafe conditions".
The mine is currently closed and rescue teams have been pulled out for now.
Mamokgethi Molopyane, a mining specialist, says there seems to be a high number of seismic activities, "which is concerning, given that we have been mining for so long and some of the technology was pioneered, here".
Wellsted said they were in the process of contacting the families of the four miners who had died.
Another employee had been located, but two remained unaccounted for Friday morning. They will be put back in soon once we have done our assessment.
Zachary Cruz, brother of Parkland shooter, arrested
Cruz was also subjected to sleep deprivation tactics and had to wear a restraint vest at all times, the group said. He was ordered to stay away from the Parkland school and all other schools after a March 19 arrest.
He said the rescue operation would go on through the night. "Yet we are not able to ensure the safety of miners".
He said 10 of 13 miners who were trapped have been freed and six are at hospital.
Rescue operations have entered their second day at Sibanye-Stillwater's Driefontein mine in Carletonville‚ near Johannesburg.
"The tremors that took place were quite distant from the area".
"Mine rescue teams were immediately mobilised and three employees have been located and have been interacting with the rescue teams".
Earlier this year, 955 miners were trapped following an electricity outage at the Sibanye Gold mine in Welkom.