Doki Doki Exit Music is a Natsuki-based mod created by Lucy.
The main character in this story decides to wake up Sayori, instead of going to school with Natsuki's cupcakes. This allows an entirely new story to be created, since Sayori lives and Monika doesn't restart the game. Not to mention that Monika doesn't appear to know about the fact that she's inside of a game.
As the main character begins to spend time with Natsuki, the abusive nature of her relationship with her father becomes more detailed. The character will attempt to help Natsuki.
Doki Doki Exit Music has been blacklisted by the DDMC subreddit due to the controversial use of covers of copyrighted music tracks.
Exit Music: Redux
On April 29, 2020, it was announced by Exit Music's creator on the Doki Doki Modification Club Discord server that a project to remake the mod was underway. The mod's remake is named Exit Music: Redux.
Please see here for more info: Exit Music: Redux