It could be that Alexis is being influenced by someone else. There might be a third character who has their own agenda and convinces Alexis to go after Beckett. Also, Alexis might have some internal issues, like self - esteem problems. If Beckett is constantly achieving things that Alexis feels she can't, it could lead to feelings of inadequacy and then the urge to bring Beckett down.
He could also gather evidence of Alexis' attempts to hurt him. If it comes to it, he can use this evidence to expose her actions to those around them, like mutual friends or authorities in their fictional world. Another way is for Beckett to strengthen his own defenses, both physically if it's a more action - oriented fanfic, and mentally by not letting Alexis' actions get to him.
She could be defensive of Beckett. Since Alexis probably has a good relationship with Beckett, she may try to convince Castle that he's wrong and that Beckett didn't mean any harm. For example, she might tell Castle about all the positive things Beckett has done for her.
Alexis might confront Beckett directly. She could say something like 'I think you're cheating on me. What's going on?' This is a very straightforward approach.
A common theme is friendship. Many fanfics explore how Beckett and Alexis become friends and the bond they share. Another theme is growth, as they both develop as characters within the fan - created stories.
Well, without having read the actual 'beckett and alexis killed fanfic', it's difficult to give a detailed account. However, generally speaking, it might be a piece of fan - made fiction that focuses on a plot where Beckett and Alexis are somehow related to a killing. Maybe they are the ones who do the killing, or perhaps they are witnesses or victims in a more complex scenario.
Maybe Alexis has a different vision of the original story or characters. Fanfic often takes creative liberties that might not align with Alexis's view of Beckett.
It could be that Castle is overprotective. He loves Alexis so much that even the slightest sign of Beckett not being on the same page as Alexis in Castle's eyes makes him think Beckett hurt her. Maybe Beckett gave Alexis some career advice that Castle thought was too pushy.
In the fanfic, it could be that there are signs that Beckett is hiding something. Perhaps he has unexplained absences. He might say he's at work but Alexis can't reach him during those times. Also, he could be overly protective of his phone or personal space, which makes Alexis suspect that he's cheating.
Love and acceptance is also a prevalent theme. Since Beckett comes into Castle's life and becomes part of Alexis's world, fanfics may focus on how they all learn to love and accept each other fully. This could involve storylines where there are initial misunderstandings but eventually they come to a place of complete acceptance and harmony in their relationships.
Common themes in fanfic usually revolve around relationships. For Alexis Hurts Beckett fanfic, it could be a complex relationship filled with misunderstandings that they have to overcome. There might also be themes related to power dynamics if one character has more power or influence than the other. Another possible theme could be self - discovery, as they interact with each other and learn more about themselves in the process.