In some fanfics, when Harry leaves the Dursleys, he might immediately feel a sense of freedom. He could start exploring the wizarding world more independently, without the constraints of his Muggle relatives. Maybe he'd meet new friends or allies earlier than in the original story.
One reason could be that he discovers a new threat and decides he can't stay with the Dursleys any longer for their safety. Another might be that he simply can't bear their mistreatment anymore and finds an opportunity to escape.
They are often portrayed as the villains. Their years of treating Harry badly are brought to light. They might look scared and out of place in the wizarding courtroom, with all its strange sights and magic.
In this fanfic, the Dursleys may be depicted as being in over their heads. Vernon Dursley, for example, might be shown as constantly angry and trying to assert his authority in a situation where he has none. Petunia Dursley could be portrayed as being torn between her dislike for magic and her sense of family obligation towards Harry. Dudley might be shown as being bullied or affected in the Muggle world because of Harry's presence in their family.
The abuse makes Harry more cautious. He has learned from the Dursleys that the world can be cruel, so he's careful about who he trusts. For example, he might be hesitant to open up to new people he meets at Hogwarts.
In many of these fanfics, there could be a new character introduced, like an old wizard who lives in the neighborhood secretly and notices Harry's situation. This character might play a crucial role in helping Harry deal with the Dursleys and his growing magical powers. He could be a mentor figure for Harry, guiding him through the tough times.
A great 'Harry Potter Dursleys fanfic' might explore the Dursleys' backstory more deeply. For example, it could show how Vernon's hatred for magic and strange things developed over time. Or it could focus on Petunia's envy of Lily's magical abilities and how that affected her relationship with Harry. Some fanfics also imagine a scenario where the Dursleys are magically transported to Hogwarts and have to adapt to the magical environment. They would be completely out of their element, and it would be interesting to see how they interact with the students and teachers.
Well, Sirius Black could be an interesting character to put in a 'Harry Potter Dursleys fanfic'. Since he was Harry's godfather, his presence could stir things up for the Dursleys. He might be furious at how they treated Harry and take some sort of action. Hermione and Ron could also be included. They could visit Harry at the Dursleys' and be shocked at the living conditions. Their reactions and how they interact with the Dursleys could make for an exciting plot. And of course, the Weasley family as a whole. Their warm and loving nature would contrast greatly with the cold Dursleys.
In a fanfic, the Dursleys might face charges for their mistreatment of Harry. They could be put on trial by the wizarding world for things like emotional abuse and neglect. For example, they made Harry live in a cupboard under the stairs and treated him like a servant. They might be found guilty and face various punishments, such as having their magic - related memories modified or being exiled from the wizard - protected areas near their home.
Definitely Dudley. In fanfic, he can be developed in so many different ways. He could become a wizard himself, or he could befriend Harry in a more meaningful way than in the original books. Another interesting character is Petunia. There could be more exploration of her past and her relationship with Lily, which can make her character more complex.