The 81-year-old was undergoing the operation at a private New York clinic last Thursday, when she started suffering from complications.
The comedian was then placed into a medically induced coma, with her family in desperate shock at the tragic turn of events.
JOAN RIVERS ON LIFE SUPPORT: FAMILY FACE DECISION TO SWITCH OFF MACHINE
Following confirmation of doctor's beginning the 48-hour process to get her off life support, daughter Melissa released a statement to thank the public for their ongoing support.
'My mother would be so touched by the tributes and prayers that we have received from around the world,' she said.
'Her condition remains serious but she is receiving the best treatment and care possible. We ask that you continue to keep her in your thoughts as we pray for her recovery.'
CELEBRITY BIG BROTHER'S CLAIRE KING HOSPITALISED AFTER MYSTERY ILLNESS
However sources have described Melissa as 'totally hysterical and is at a loss for what to do', amidst reports that 'Rivers would not want to live unless she could enjoy a full and active life' without being a 'burden on anyone.'
Now Rivers' family are said to be considering bringing a lawsuit, as doctors fear a stroke could leave her 'as a vegetable' or 'needing a wheelchair'.