One idea could be that the character discovers a hidden Horcrux in a place no one expected, like in an old, abandoned wizarding prison. They have to face numerous dark magic traps alone. Another could be that they are being hunted themselves while on the Horcrux hunt, adding an extra layer of danger.
A possible plot for a Harry Potter Ghost Hunt fanfiction is that a group of students start seeing strange apparitions that seem to be leading them to a hidden chamber in Hogwarts. As they follow these ghostly figures, they realize that it's a test set by one of the founders of Hogwarts. If they succeed in the hunt and reach the chamber, they will be rewarded with a powerful magical artifact. Maybe it could be a wand that has the ability to control certain types of magic better than any other wand. Or perhaps a cloak that not only makes the wearer invisible but also provides protection from dark magic spells.
Well, a possible plotline is that they discover a Horcrux in a place that was previously thought to be just a mythical or lost location. Maybe it's hidden in an ancient wizarding ruin that has been long forgotten. As they search for this Horcrux, they encounter all kinds of magical creatures and traps. And also, their relationship might develop romantically during the hunt. They share moments of fear and triumph which bring them closer together.
Well, perhaps in this fanfiction, it explores the magical implications of Harry being a Horcrux. For example, how it affects his connection to Voldemort's magic and whether it gives him some unexpected powers or vulnerabilities. Also, it could show how the Order of the Phoenix or Dumbledore's Army react when they find out this shocking truth about Harry.
Neville could also be an excellent choice. He has shown great courage throughout the series. His knowledge of Herbology could come in handy when dealing with Horcruxes that might be hidden in or protected by plants. And his growth from a shy boy to a brave young man would make for an interesting arc in a solo Horcrux hunt story.
One interesting plot twist could be that the last Horcrux is not an object but a person no one suspected. For example, it could be a seemingly innocent bystander who has been under Voldemort's control all along without anyone realizing.
One interesting concept is the idea of creating new Horcruxes. In some fanfictions, a character might attempt to create a Horcrux in a different way than Voldemort did, perhaps using a more unique object or spell. Another concept could be the destruction of Horcruxes in unexpected ways. For example, a fanfic might explore if a Horcrux could be destroyed by a powerful emotion rather than a specific magical weapon.
One idea could be that Harry discovers a hidden magic within himself that no one else has. He has to battle alone against dark wizards who are after this power. Another could be that he's sent on a secret mission where he can't rely on his friends, and he battles ancient magical creatures all by himself.
It can completely change the direction of the plot. For instance, if Harry absorbs the Horcrux early on, he may have to face different challenges than in the original story. He might become a target for both sides, as the good side could be wary of his new, Horcrux - influenced state, and the bad side might see him as a threat to Voldemort's power.
The relationships between characters would also be altered. Hermione and Ron might be even more protective of Harry, but also more suspicious. They would constantly be on the lookout for any signs that the Horcrux is influencing Harry negatively. Dumbledore's plans, if he were still alive in the fanfiction, would have to be completely re - thought. The prophecy might take on a new meaning as well, since Harry now has a part of Voldemort's soul within him. All in all, it's a major plot - twisting concept.
Another concept could be centered around the characters' reactions when they finally locate the seventh horcrux. There could be internal struggles among the characters, like Harry having doubts about whether destroying it is the right thing to do, considering it might hold some knowledge that could be useful against Voldemort.