The Dementor Lady of Azkaban, Sylvia, has two secrets. First, she failed to report that the prisoner Black is an Animagus. Second, her consciousness is fading, and she is about to become a monster without emotions.
A woman who claims to be a prophet tells her that she can sign a soul contract with a sentient being. That would give her a physical body and save her from having her consciousness disappear.
Within hundreds of miles of Azkaban, the only person who seems able to make a contract with her is Black, who desperately wants to break out of prison for revenge and is willing to give everything.
After a long conversation, the two agree to work together. But a small hitch arises with the soul contract: Black's lifelong wish remains unfulfilled, so his soul cannot fully separate from him.
So she strikes a new deal with that stupid dog. She will help him get close to Harry Potter and catch Peter Pettigrew, and afterward, Black will give that piece of his soul to her completely.
Gradually, she discovers that the contract she signed with that stupid dog was no ordinary soul contract. It was a marriage contract!
What's more, before she became a Dementor, she seems to have been a witch, and one connected to Black. She was his dead ex-girlfriend!
Bonus scene: When Remus Lupin goes to Honeydukes in Hogsmeade to buy Harry some chocolate, he suddenly spots his wanted brother in a newly opened bookshop nearby, being led by the girlfriend who died fourteen years ago. What a horrifying sight...
OOC warning: Anything unreasonable is my own invention. Please don't flame me if you dislike it.