Maybe they believed that Hermione had some sort of special power even as a baby that could be both a danger and an asset. By kidnapping her, they could control and train her in a way that would benefit the fight against the Dark side. For example, if she was showing signs of extremely powerful magic at a young age, they may have wanted to ensure she used it for good from the start.
She might use her intelligence and magic skills. For example, she could create a distraction using a spell like 'Confundo' on her captors and then make a run for it. Hermione is known for her quick thinking, so she could also find a loophole in the security measures set by the Order.
There could be. Fanfiction writers love to explore different scenarios that deviate from the original story. But it's important to note that this goes against the general perception of Dumbledore's character. In the official Harry Potter series, Dumbledore is a protector, not a kidnapper. But in the world of fanfiction, anything is possible.
One possible motive could be power. In some fanfictions, there might be dark wizards or witches who believe that Hermione, being a very intelligent and magically gifted child even from a young age, could be used to their advantage. They might think that they can control her magic or use her knowledge for their evil plans, like finding ancient magical artifacts or unlocking powerful spells that are otherwise inaccessible.
They could have been put under some sort of spell by the Order to forget about Hermione. In that case, they would have just gone on with their lives, completely unaware that their daughter had been taken. However, if the spell was not perfect, they might have had some strange feelings or dreams about a missing child.
Often, the story will focus on the search for Hermione. Her parents would be desperate and might enlist the help of the wizarding authorities. Harry and Ron, when they grow up and learn about this, could also become deeply involved in the search. There might be clues left behind by the kidnappers that lead them on a wild adventure through different magical locations.
Typically, there's the kidnapped character who is the main focus. Then there's the kidnapper, who can be a complex character with various motives. There might also be side characters like other captives or people who are trying to rescue the kidnapped one.
In the fanfiction world, such themes are generally considered unethical. Fanfiction is often a form of creative expression within a community, and themes of kidnapping and torture go against basic moral values. It can also be disturbing to many readers.
One common trope is the heroic rescue. Usually, her friends like Harry and Ron will come to her rescue in a daring adventure. Another is the 'damsel in distress' aspect, although Hermione is far from a typical damsel. Sometimes, the kidnapper might have some hidden motives related to her intelligence, like wanting to steal her knowledge.
Hermione could use her intelligence to outwit Bellatrix. She might pretend to be compliant and gradually gain Bellatrix's trust, all the while looking for an opportunity to escape. For instance, she could trick Bellatrix into thinking she has some important information that can only be retrieved in a certain location, and then make a run for it when they get there.