One possible plotline could be Petunia struggling to make ends meet while raising Dudley on her own. She might have to take on extra jobs in the Muggle world, and this could lead to some interesting interactions with her neighbors. Another could be her dealing with Dudley's magical abilities (if he has any latent magic), which she has no idea how to handle.
Well, a plotline could revolve around Petunia trying to keep Dudley away from the wizarding world out of fear, yet still having to face some magical elements that seep into their lives. For example, strange letters or magical creatures showing up. Or perhaps she could start to question her own sister's choices more, now that she's in a similar situation of single parenting, and this could lead to her having a change of heart towards Harry.
A possible plotline might be Petunia having to deal with the judgment of the wizarding world, as they might look down on a Muggle single mother. She could then try to prove herself and Dudley's worth. Another aspect could be her trying to find love again while also being a single mother, and how this new relationship could either bring her closer to or further from the wizarding world. There could also be a plot where she discovers some long - hidden family secrets that change everything she thought she knew about her family and the wizarding world.
There are indeed some. However, the quality can vary greatly. Some fanfics might depict Petunia as a more sympathetic single mother, showing how she copes with raising Dudley alone. Others may explore how her knowledge of the wizarding world (even if limited) affects her parenting. It's really a matter of exploring different works to find ones that suit your taste.
A plotline could involve Petunia having a change of heart due to a magical event. For instance, she might accidentally stumble upon some of Harry's magic or receive a message from the wizarding world about his importance. This could lead her to stand up against Vernon and protect Harry. She could then start to teach Harry about his mother's side of the family and the magic that runs in his veins in a more positive way than the Dursleys ever did. And perhaps she even helps him develop his magic skills secretly before he goes to Hogwarts.
Maybe the fanfic could involve Bulma meeting someone who is initially hesitant to get involved with a single mother but then gradually falls in love with her and her child. Another plotline could be that Bulma's ex - the father of her child - resurfaces and creates complications in her new dating attempts.
A possible plotline could be that Draco, out of curiosity, starts to research Harry Potter's mother. As he delves deeper, he finds out about her selfless love and her powerful magic. This makes him question his own values and beliefs, leading to a transformation in his character.
One possible plotline could be a love - at - first - sight scenario where Porky Pig is smitten with Petunia and tries to court her in his bumbling but endearing way.
One possible plotline could be that Petunia has a sudden realization of how unfairly she has treated Harry over the years and tries to make amends. She might start by secretly helping him with things around the house or protecting him from Dudley's bullying.
One possible plotline could be Harry coming to power after a great war in the wizarding world. He then has to deal with rebuilding and unifying the different wizarding communities under his rule as emperor. He might face resistance from some traditional wizarding families who don't want to accept a new form of government.
In a 'Harry Potter is an assassin' fanfic, the plot could start with Harry being trained by an unknown and powerful wizard who has his own motives for creating an assassin out of Harry. This trainer could be someone from a far - off land or an ancient order. Harry then starts taking on targets within the wizarding world that are supposedly 'evil' but as he delves deeper, he realizes that things are not as black and white as he was told. His friends start to notice his strange behavior and he has to either come clean or keep lying to them. As the story progresses, Harry might have to make some tough choices between his loyalty to his friends and his new - found assassin duties, all while uncovering secrets about the wizarding world that were previously hidden.
One possible plot could be that Petunia is somehow magically enslaved by a dark wizard. Harry, upon finding out, feels a sense of obligation to save her. He might have to use his knowledge of magic and his connections at Hogwarts to figure out a way to break the spell. Along the way, he could discover some secrets about Petunia's past that were related to the wizarding world.
In a non - offensive and family - friendly fanfic idea, perhaps Petunia Dursley discovers a magical cock cage (not in a vulgar way) that has some connection to the wizarding world. Maybe it was left by a wizard who visited Privet Drive by mistake. Petunia, being the nosy character she is, tries to figure out what it is and how it works. This could lead to a series of comical events as she fumbles with this strange magical object, all while still maintaining her strict, Muggle - like personality.