Yes, it's possible in fanfiction. It could be justified as self - defense. If a dementor was about to attack an innocent, especially someone Harry cared about, he might be pushed to use a powerful spell to kill it rather than just the Patronus charm which usually just drives them away.
Sure, it can happen in fanfiction. It could be justified by the idea that the dementor was somehow corrupted beyond the normal state, like it was being controlled by a more powerful dark wizard to be extra - deadly. So, Harry, in order to protect the greater good, had no choice but to kill it. Another way could be that Harry discovers a new, more powerful magic that accidentally kills the dementor while he was trying to subdue it in a different way.
One possible plot could be that Harry's mother was secretly researching dementors for some noble reason, like finding a way to cure their 'evil' nature. She might be collecting information about them, which could put her in danger as dementors are not to be trifled with. This could then lead to a series of events where her knowledge is passed on to Harry in some way, and he has to continue her work.
Well, in the fanfic world, the author might have given Harry the ability to use Godric's sword against dementors. Maybe the sword has some special enchantment in this story that makes it effective against the soul - sucking dementors.
Well, it could be about a Harry Potter who has some special power over Dementors. Maybe he can control them instead of just fending them off with a Patronus. He could use this new - found power to his advantage in the wizarding world, like using Dementors to guard against dark wizards.
Harry Potter can be seen as a superhero. He has powers that are unique to his world, magic. He uses these powers to protect his friends, Hogwarts, and the entire wizarding world from the forces of evil. Just like a superhero, he has a sense of justice and is willing to risk his life for the greater good.
In some fanfiction, the idea of Harry Potter being betrayed by his parents might be justified through a complex web of magic and prophecy. Maybe the parents thought sacrificing Harry was the only way to save the wizarding world from a greater evil. However, this goes against the essence of their characters in the original books.
One possible plot is that Harry absorbs the dementor in a moment of extreme danger. This changes him in some ways. His Patronus might become more powerful as a result. He may also start to understand the dementors' origin and find a way to stop their creation. He could then share this knowledge with the wizarding world.
Maybe it's a rogue group of wizards who fear Harry's power over Dementors. They might think that Harry is going to use the Dementors to take over the wizarding world in an unjust way. So they band together to try and stop Harry before he can fully embrace his role as the King of Dementors.
One possible motive could be extreme revenge. After years of being mistreated, locked in a cupboard, and generally being made to feel unwanted, Harry might snap in fanfiction. Another could be a sense of self - preservation if the Dursleys were somehow involved in a plot against Harry's life in the fan - created plot.
One possible motive could be a misunderstanding. Maybe Snape is framed for something really bad, like a dark magic plot against Hogwarts. Harry, in his haste to protect the school and his friends, believes Snape is guilty and takes drastic action. Another reason could be if Snape accidentally endangers someone Harry loves dearly, like Ginny or Ron, and Harry's emotions get the better of him in the heat of the moment.
It could be due to a blood - magic related incident. Suppose there is some long - lost connection between Harry's family and the origin of Dementors. A spell or a ritual that awakens this connection might endow Harry with Dementor - like powers. For example, if there was an ancestor who was involved in the creation of Dementors in some way, and that knowledge or power was passed down in a latent form in Harry's blood.