There were some musings about reusing old unreleased tracks for Midnights but I think a big part of the CONSPIRACY is something different. That she had a full front-to-back album ready for release but shelved it. This has been a popular theory in swiftie fandom for some time now.
The theory goes: Taylor had a full album ready for release in late 2016, which would match with her traditional album release cadence of 2 years (1989 was released in 2014), but decided to shelve it when the whole Kimye drama blew up mid 2016. She then disappeared for a year to avoid more public scrutiny, wrote Reputation in secret, and released it late 2017. Reputation directly addressed the 2016 happenings, as well as her new budding romance which occurred during the same time period. It also had a distinctly darker sound and image than any of her previous eras.
This "lost" album is supposed to be named
Karma.
There's some sense and logic in the idea that Taylor would not have wanted to put out another happy, upbeat pop album at a time when her mood did not match those sentiments. However there were clues that fans latched onto. For one, Taylor had just (April 2016) debuted a new look, with her hair bleached and cut short after a Vogue photoshoot. This look was dubbed "Bleachella":
(at the time fans hated this look, but nowadays of course reminisce for it).
There was also this picture she posted wearing the logo used for the recent hit Rihanna single "This Is What You Came For", produced by Taylor's then boyfriend Calvin Harris:
At the time she posted this picture it had not yet been confirmed that Taylor actually wrote this song, but there were rumors, since her voice can be heard in it as background vocals, and the credited writer of the song was the pseudonym Nils Sjöberg that no one could find any info on.
So this new look and kinda new music from Taylor got fans thinking a new era was right around the corner, possibly with some collaborations with Calvin Harris.
But Taylor and Calvin broke up shortly after this, then the Kimye drama happened, and Taylor disappeared for awhile. 2016 passed with no new album.
But there's more. Where did fans get the idea that the album would be called "Karma"? Well, in Taylor's "73 Questions" interview with Vogue she answered the question "What do you think is the most important life lesson for someone to learn?" with "That karma's real". But mostly it comes from this scene in "The Man" music video from Lover:
Here you can see many of her album titles as graffiti on the wall with KARMA in the middle. There's also the "MISSING" poster right next to it. Read this tweet thread if you want to get an idea of the unhinged theories around this:
https://nitter.net/kindagoldrush/status/1406348027674169348
Anyway the main reasons fans thought Midnights might actually be the long lost Karma album is because of this video Taylor posted in her "Midnights Mayhem With Me" series, where she revealed the track titles on the album one by one:
Her breaking out in laughter at the end of that convinced some swifties that this was it. I think she was just laughing at the masterful troll job she dropped on her fans.
So that's the conspiracy mostly. Surely the theories will continue cuz it really does not seem like Midnights is actually Karma, besides for the named track. Maybe another album.
BTW, there's another secret album swifties are convinced Taylor is secretly guarding. It's called "Woodvale" and was supposed to be the 3rd surprise release in the Folklore Evermore series. Perhaps that's a story for another time.