The sick singer was donated the kidney by Patty Argueta's sister, Jessica, after she died from complications related to childbirth.
Patty told Larry King that organ donor Jessica, who died at the age of 32, had been a big fan of Cole's before passing away last year and would have wanted the singer to have her kidney.
'She liked the duet Unforgettable to the point that the CD doesn't exist anymore, because we've run it over and over,' Argueta recalled as she sat beside Cole on King's CNN show.
'I mean, I'm happy that she lives through so many people. That I can feel a connection when Natalie - it brings us - of such a tragedy and loss, it's amazing that she still lives on.'
Cole had come across Jessica's aunt, a nurse, while getting treated for her kidney troubles.
And when Jessica passed away they recalled Cole and her fight and the family made a direct organ donation to the singer.
Cole said: 'I just thought that the whole thing was just - it was very overwhelming. It was a very emotional time, especially because Patty and I already had so much in common. We had both lost our sisters, you know, so I knew how she felt already.'
Cole has said her kidney troubles go back to February 2008 when she was diagnosed with Hepatitis C. She blames the condition on her battles with cocaine and heroin.