In some fanfictions, Snape kills Dumbledore as part of a greater plan. Maybe Dumbledore was already dying or had some sort of incurable dark magic on him, and Snape's act was a mercy killing. It could also be a complex plot twist where Snape is actually trying to protect the wizarding world from a greater threat that only he and Dumbledore knew about.
It changes Harry's view of Snape completely. Harry already had a very complex relationship with Snape, but this act would make him see Snape as an even greater enemy. He would be filled with rage and a thirst for revenge. Hermione and Ron would also be very affected. They would support Harry in his quest to avenge Dumbledore and would see Snape as a traitor to the wizarding world.
In many such fanfictions, Dumbledore might comfort Snape by reminding him of his good deeds. For example, he could say that Snape's role as a double agent is crucial for the greater good. Dumbledore might also offer a sympathetic ear, listening to Snape's inner turmoil about his past actions and his love for Lily. By validating Snape's feelings and his importance in the fight against Voldemort, Dumbledore provides comfort.
The tragedy of their relationship also draws people in. Snape's love for Lily and his loyalty to Dumbledore despite his difficult past make for great fodder for fanfiction. Writers can explore how their relationship might have developed differently or how they truly felt about each other behind the scenes of the main story.
Dumbledore can hurt Snape in fanfiction by taking advantage of his love for Lily. He might use this love as a tool to manipulate Snape into doing dangerous tasks. For example, making Snape spy on Voldemort, knowing full well that Snape's life is at risk every time he does so.
In the fanfiction, Snape could protect Harry from Dumbledore by using his skills in potions. For example, he might create a potion that hides Harry's magical signature from Dumbledore's detection. Or he could use his knowledge of the Dark Arts to counter any spells or charms that Dumbledore might use to keep tabs on Harry. Snape is very intelligent and resourceful, so he could find various ways to physically and magically shield Harry from Dumbledore.
Typically, it portrays Dumbledore as a manipulator. He's seen as using Snape's feelings for Lily and Harry's role in the fight against Voldemort for his own purposes, rather than having pure intentions.
Yes, it is a somewhat common theme in some fanfictions. One reason could be the complex relationship between Harry and Snape in the original series. Snape was often cruel to Harry, so in some alternate universes, writers explore the extreme scenario of Harry killing Snape. It also allows for exploring darker aspects of Harry's character and the consequences of such an act within the wizarding world.
Yes, in the vast world of fanfiction, there could potentially be such a story. Fanfiction often takes creative liberties with the original characters and storylines. However, this would be a very dark and non - canonical take on the Harry Potter universe.
One common way is by giving Snape hope. Dumbledore could talk about the end of Voldemort's reign and how Snape's part in it is essential. For instance, he might say that Snape's knowledge and skills are the keys to victory. Another way is by showing trust. Dumbledore might entrust Snape with more important tasks or secrets, which makes Snape feel valued.