Definitely not. The manga follows the volleyball journey and development of the characters, and Hinata remains an important part throughout without facing death.
A common theme is friendship. Their relationship on the volleyball court is a strong base for a great friendship in these fanfics. Another is growth. They both grow as players and as people because of their interactions. And teamwork is also often highlighted, as they are a crucial duo in the team.
Growth is also a prevalent theme. Both Hinata and Yachi grow as individuals in the series, and in fanfiction, their relationship is often part of that growth journey. For example, they might help each other overcome insecurities and become better versions of themselves.
Hinata might be very hurt. She's a sensitive person, so Naruto yelling at her could make her feel small and sad. She might start to doubt herself and her abilities.
At first, Hinata's reaction might be one of shock and disbelief. She has probably never expected Sasuke to do such a thing. However, she is a strong - willed character deep down. So, she might start to plan her escape. She could use her knowledge of the ninja world and her own family's techniques. She might also try to find out if Sasuke has any allies or if there are other forces at work. She could try to turn the situation around and make Sasuke realize that what he is doing is wrong by appealing to his better nature or by using her own skills to outwit him.
You can find 'Haikyuu Hinata x Kageyama' fanfics on Archive of Our Own (AO3). It has a large collection of fanfics from various fandoms, and the search function makes it easy to find specific ones like those about Hinata and Kageyama.
One great 'Haikyuu Hinata x Kageyama' fanfic is 'The Bond Beyond the Court'. It focuses on their relationship growth not just in volleyball but also in their daily lives. It shows how they support each other through different challenges.
Kuroo doesn't meet his demise in the manga. The plot doesn't involve his death. He continues to play an important role and contribute to the story's development.