In certain fanfictions of this type, Harry could be found by a powerful but reclusive wizard. This wizard decides to mentor Harry in the ways of ancient and lost magics. Harry then uses this knowledge to not only become a very powerful wizard but also to change the wizarding world's view on things like blood purity. He may also go on a journey to find out why the Dursleys abandoned him and in the process, uncover some dark secrets about his family that had been long buried.
One possible plotline could be Harry finding a new family among the magical creatures. For example, he might be taken in by a friendly centaur herd who teach him their ways of magic and survival. Another could be Harry being found by a secret group of wizards who are against the Dursleys' cruel treatment and they help him develop his magic in a more positive and nurturing environment. And there could also be a plot where Harry discovers a hidden magical power within himself as a result of the abandonment, like the ability to communicate with the spirits of Hogwarts, which then guides him on a new path to face Voldemort.
One possible plotline could be Harry finding a way to break free from the chains and use his magic to confront the Dursleys about their mistreatment. Another could be the Dursleys realizing the error of their ways after chaining Harry up and having a change of heart. Or perhaps there are magical forces at work that lead to a series of adventures while Harry is still chained, like dealing with strange creatures that are attracted to the situation.
One possible plotline could be Harry discovering a hidden magical ability that helps him escape. For example, he might find out he can teleport short distances, which he uses to get away from the Dursleys' house when they are being particularly cruel. Another could be that he gets help from an unexpected magical creature that has been secretly observing him all along. Maybe a house - elf that takes pity on him and shows him a secret passage out of the house.
One possible plotline could be Harry growing up in an American wizarding community that has different traditions and values compared to the British one. He might have to adapt to new spells and magical practices.
One interesting plotline could be Harry showing early signs of magic that the Dursleys try to suppress. For example, he might accidentally make Dudley's toys float when he's angry or frustrated.
One possible plotline could be that the Dursleys start to show their love by secretly protecting Harry from the wizarding world's threats. Maybe they learn about a dark wizard targeting Harry and use their Muggle ways to keep him safe without him even realizing it.
Well, in some fanfictions, Harry might control the Dursleys by making them understand the wizarding world. He could show them magical things and, as a result, they start to respect him and his abilities. This could lead to a whole new dynamic in the household, where the Dursleys are no longer mean but rather in awe of Harry and his magic.
One possible plotline could be Harry using his newly discovered magical abilities in unexpected ways against the Dursleys. For example, he might make the Dursleys' dinner plates fly around when they are being particularly mean to him.
One possible plotline could be Harry finding a magical way to fight back against the Dursleys' torture while still hiding his magic from the Muggle world. For example, he might use some subtle magic to make things go wrong for the Dursleys when they are being especially cruel. Another could be that his Hogwarts friends discover what's going on and come up with a plan to rescue him during the holidays. Maybe Hermione uses her knowledge of the law to find a way to legally remove Harry from the Dursleys' custody.
In some fanfictions, the Dursleys might be portrayed as having a change of heart. For example, they could start to secretly admire Harry's magical abilities instead of resenting them. This can add an interesting twist to the original story.