Emergency workers say other miners at the site near Johannesburg refused to come out of the shaft because they fear arrest. Another 12 miners were rescued on Sunday.
Emergency responder Kobus Du Plooy said: “Should they have a change of heart and mind, they then have at least some access to get out of the shaft.”
It was unclear how long the miners, who seemed to have few options, planned to prolong their stay in the mine.
Some of the 11 who came out were dehydrated but otherwise in good health.
They were believed to have been trapped since Saturday morning and police patrolling in the area heard their screams for help, the South African Press Association reported.
Rescue vehicles and equipment were brought to the site to stabilise the ground before the removal of the rubble began.
Illegal mining
Authorities suspect the miners in Benoni were robbed by a rival group that blocked the mine exit, reported Eyewitness News, a South African media outlet.
Illegal mining remains a serious concern, despite progress in curbing it, South Africa’s mineral resources department said in a statement. It attributed the improvement to “illegal mining forums”, in which stakeholders in the mining industry seal open shafts and seek to detain illegal miners, according to the South African Press Association.
Some analysts say the problem could increase if legal mines close or downsize, forcing skilled workers who have lost their jobs to turn to illegal activities. South Africa’s mining industry, a pillar of the economy, is struggling with rising costs. Tens of thousands of workers in the platinum sector are currently on strike.