Well, in certain 'harry gets saved fanfiction', Hermione might use her vast knowledge of magic in a completely new and unexpected way to save Harry. She could combine different spells and charms that no one has thought of before. Also, there could be fanfictions where Neville, having grown in confidence and power, is the one who saves Harry from a life - threatening encounter with a dark wizard.
Hermione is a very common character. Given her intelligence and magical skills, she often plays a crucial role in saving Harry. Ron is also often involved as Harry's loyal friend. Dumbledore, even in fanfiction, is a character who might show up to save Harry or at least guide the others in the rescue.
One interesting story could be where a group of Slytherins, against the common perception of their house, secretly protect Harry during a dangerous encounter in the Forbidden Forest. They use their cunning and knowledge of the forest's secrets to keep him safe.
One interesting 'harry gets summoned fanfiction' could be where he is summoned to an alternate magical realm. In this realm, he has to face new challenges and enemies that are different from what he encounters in the original Harry Potter world. For example, he might have to deal with a powerful dark wizard who has unique and strange magic.
A great 'harry gets adopted fanfiction' idea could be that he is adopted by a Muggle family who are actually descendants of a squib. They know about the wizarding world but are living in the Muggle world. This would give Harry a chance to see how the two worlds can co - exist in a more harmonious way within a family unit.
One interesting story could be Harry getting a tattoo that represents his connection to his parents. Maybe a stag for his father and a lily for his mother. It could be a way for him to carry their memory with him in a more permanent and visible way.
One possible plotline could be that Harry gets grounded for accidentally using magic outside of school in a Muggle area. This might lead to him having to deal with the disappointment of his friends who can't visit him as easily. Another could be that he gets grounded because he was caught sneaking out to follow a lead on a new dark wizard threat, and the adults in his life want to keep him safe by restricting his movements.
In some fanfictions, Voldemort might save Harry due to a complex change in his character. For example, he could discover a newfound sense of respect for Harry's power or courage. Maybe he realizes that Harry is the only one who can truly understand him, and in a moment of strange kinship, he decides to save Harry from a greater threat that is about to befall them both.
It depends on the specific plot of the vampire fanfiction. There could be a scenario where the vampire has a prophetic vision about Harry's importance to the world or to their own existence. So, to safeguard that future, the vampire steps in and saves Harry. It might also be that the vampire is in love with Harry (a common trope in fanfiction) and would do anything to keep him safe, thus saving him from various perils.
The Malfoys could save Harry in fanfiction because of a personal debt. Maybe Harry once unknowingly did something that benefited the Malfoys greatly. This could be as simple as preventing a disaster from befalling their family business or saving the life of a family member secretly. When the time comes, the Malfoys feel obliged to return the favor and save Harry from whatever danger he is in. Also, it could be part of a complex plot where the Malfoys are trying to redeem themselves, and saving Harry is a big step in that direction.
In some fanfictions, Harry might be saved by NCIS through their excellent investigative skills. They could uncover a plot against Harry in time, using their resources to track down the bad guys before any harm comes to Harry.