Well, in fanfiction, anything can happen. Regarding Dumbledore stealing from Harry, it depends on the specific fanfic. Some might show Dumbledore stealing Harry's inheritance, perhaps believing he can use it for a greater good. But this is not in line with the general perception of Dumbledore in the main series. Fanfic writers like to twist and turn the characters to create new and interesting stories.
One possible motive could be a misguided sense of protection. Dumbledore might think that taking something from Harry, like a powerful magical item, would keep it out of the wrong hands. He may believe that Harry is too young or inexperienced to handle it properly.
In a fanfiction, Dumbledore might steal out of desperation. Suppose there was a situation where a curse was about to be unleashed on Hogwarts, and the only way to stop it was by stealing a particular ingredient for an antidote from a place where it was not supposed to be taken. Dumbledore, seeing no other option, decides to steal it. His motive here is to save the school and its students, even if it means breaking the rules.
One possible reason could be that Dumbledore believes he is acting in Harry's greater good. Maybe he thinks that by taking certain items from Harry, he can protect them from falling into the wrong hands. For example, if Harry has a powerful magical artifact that Voldemort desires, Dumbledore might steal it to keep it safe.
The fanfic changes the perception of Dumbledore's character in that it shatters the image of his infallibility. He is no longer the perfect headmaster and guide. Stealing from Harry shows that he is capable of moral wrongs, and this can lead to a more nuanced understanding of his character, where he is not simply all - good or all - bad but a mix of both, with his own motives and desires that might not always align with what is best for Harry.
I'm not sure if there is a specific 'Harry Potter Dumbledore Stealing Fanfiction' out there. However, if there were, the plot could potentially involve Dumbledore stealing something important like a powerful magical artifact that he believes is necessary to protect Hogwarts or the wizarding world from a great evil, but his actions are misinterpreted by the characters in the fanfiction.
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.
One possible reason could be that Harry has discovered something about himself or his past that he thinks Dumbledore might not approve of or might try to stop him from exploring further. For example, if he found out some dark magic connection in his family history that he wants to understand on his own without Dumbledore interfering.
One reason could be that Snape has his own complex sense of loyalty. He may feel that Dumbledore's plans for Harry are too dangerous or not in Harry's best interest in some ways. He has a long - standing relationship with Harry's mother, Lily, and perhaps through that connection, he wants to safeguard Harry from any harm that might come from Dumbledore's actions or decisions.
His friends like Ron and Hermione might help him. They are always there for Harry and if they believe that Harry has a valid reason for hiding from Dumbledore, they would likely do whatever they can to keep him hidden and safe. For instance, Hermione could use her intelligence to create spells or distractions to keep Dumbledore off Harry's trail.