It's very likely that such a fanfiction exists. Fanfiction is a vast and diverse world where writers can let their imaginations run wild. Since Black Cat has her own motives and character traits, and Spiderman has his enemies and challenges, a scenario where Black Cat kills Spiderman could be an interesting exploration of betrayal, revenge, or a change in the status quo. There may be multiple versions of such a fanfiction, each with different interpretations and story developments.
I'm not aware of any official 'Captain America Kills Spiderman' fanfic. This concept goes against the general heroic and friendly relationship between the two characters in the Marvel universe. However, in the realm of fan - created works, anything can be imagined, but it would be a very dark and out - of - character take.
One reason could be to create a shock factor. It goes against the typical hero - villain dynamic we expect. Another might be to explore a darker side of Black Cat's character, showing her capable of extreme actions.
One possible reason could be mind control. Maybe an enemy has the ability to control Captain America's mind and make him turn on Spiderman. Another reason might be a misunderstanding. For example, if Spiderman was framed for a crime he didn't commit and Captain America believed the false evidence.
One of the best Kraven stories is 'Kraven's Last Hunt'. In this story, Kraven hunts Spider - Man in a very intense and psychological battle. It shows his obsession and his complex character.
Kraven's back story is quite complex. He was born into a privileged life but found the normal hunting of animals to be too easy. He had an insatiable thirst for the most difficult and dangerous hunts. When he heard about Spider - Man, a being with superhuman abilities, he saw it as an opportunity to prove himself as the greatest hunter. He trained hard, using his wealth to gather all sorts of hunting equipment and knowledge. His determination to hunt Spider - Man led him to engage in many battles with the web - slinger, becoming one of his most persistent foes.
The story arc where Kraven hunts Spider - Man across New York is also great. He uses his jungle - hunting tactics in an urban setting. Kraven tracks Spider - Man's every move, setting elaborate traps. It shows his strategic mind and his ability to adapt to different environments, which is fascinating to read about.