In the 10 years since Amy Winehouse's death, a handful of her unreleased songs have been uncovered for the posthumous albums Lioness and Amy.
But most of the material she recorded is presumed to be missing, after label boss David Joseph destroyed her demos to prevent them being exploited.
"It was a moral thing," he told Billboard in 2015.
Letting other people finish her work "would never happen on my watch," he added.
"It now can't happen on anyone else's."
While many critics applauded his desire to protect Amy's legacy, her father has a different view.
"He's an idiot," Mitch Winehouse told the BBC, adding that "of course" he wanted fans to hear her unreleased songs.
But he says there may still be hope, as the family still owns some of her recordings.
"We've found a few bits and pieces but it's difficult because the CDs are a bit corrupted," he says, "but apparently we've been told we might be able to rescue something."
"It might not be as good as Back To Black but from what I've heard, from the snippets that we might be able to rescue, it's good."
"It's nice to see it," added Amy's mother, Janis Winehouse-Collins. "Amy was always singing. Always singing, constantly."
The recordings include some of the star's early, pre-fame compositions. Mitch said it would give fans a new insight into how she developed as a songwriter.
"To me, I want to hear all this stuff and I want Amy's fans to hear all this stuff so they can see she started there and she ended up here."
Janis added that, if the music were to be salvaged for release, it could be called "The Progression of Amy".
The BBC has asked David Joseph if he wanted to respond to Mr Winehouse's comments.
The music is one of several projects Amy's estate is working on, including a dramatised film of her life and a stage musical.
However, her parents admitted that, after Amy's death, it had initially been difficult for them to hear her music or see videos of her performing.
"The first five years I couldn't watch a video or listen to the music," said Mitch. It's only been relatively recently that I've been able to do that.
For Janis, however, those reminders of Amy help to keep her memory alive.
"It's a funny thing: Every day there are Amy moments," she said. "That seems to be how life is. We'll be listening to the radio: Amy. Watching TV: Amy. It's always nice. It's always nice to hear Amy."
Documentary will 'reclaim' Amy's image
The couple, who split up when Amy was about 10 years old, were speaking to the BBC in a rare joint interview ahead of the 10th anniversary of Amy's death.
They have also worked on a new BBC Two documentary, narrated by Janis, that aims to rehabilitate the singer's image.
Rather than the well-worn tales of drug abuse, addiction and destructive behaviour, it paints a picture of the funny, generous Amy they knew.
"People have a very black and white view of Amy. They thought she was a certain way… she wasn't," Mitch told BBC News.
"We wanted for people to get a different view of her, to understand she was a loving, kind and very generous person.
"You can't airbrush all the horrible stuff out. We wouldn't do that [but] we wanted to emphasise what she was really like," he added.
"Even in the times she was really ill, we got through it with a sense of humour."
The couple added that Amy's family and friends would mark her passing by visiting her grave in Edgware, with Mitch saying: "The first 10 minutes we'll be sobbing and after that we'll be in fits of laughter with a new Amy anecdote."
Janis added: "Although it's not a joyful thing that we would celebrate it, we do. We actually go and remember her. It's just nice to be there.
"My joke is 'now I know where she is'."
Reclaiming Amy will be on BBC Two and the BBC iPlayer from 21:00 BST.