Well, it could be a story about Percy being held captive by some villain who ties him to the bed frame as a way to keep him from escaping or causing trouble. Maybe the story then revolves around Percy trying to free himself and defeat the villain.
In the 'percy is tied to the bed frame fanfiction', it might also be a scenario where Percy is in a magical or alternate world where strange things happen. He could be tied to the bed frame as part of a ritual or a spell gone wrong. The story could then be about his journey to reverse the situation and get back to normal.
It could be an enemy. For example, if Percy has made some powerful foes in his adventures, they might tie him to the bed frame to interrogate him or as a form of punishment.
One possible plot could be that there is some sort of misunderstanding. Fleur believes Hermione is in danger from some dark magic or a dangerous creature and ties her to the bed to keep her safe. As the story unfolds, they realize the miscommunication and work together to solve the real issue at hand. However, this is a rather strange starting point for a plot and would need a lot of careful development to make it a believable and engaging fanfiction.
One possible plot could be that the mom has some sort of a secret that someone wants to keep her from revealing. So they tie her to the bed to stop her from going to the authorities or telling someone important. For example, she might have witnessed a crime and the criminals tie her up to keep her quiet.
One plotline could be that they are victims of a prank by some mischievous students using a new, untested spell. They then have to figure out how to break free and also how to deal with the fallout of being in such an embarrassing situation together.
I'm not sure specifically as I haven't read that exact fanfiction. It could potentially be about a conflict or a strange situation between Victoria and Bella. Maybe Victoria has some ulterior motives for tying Bella to the bed, like trying to keep her from interfering in something.
One possibility could be a situation where Fleur is under the influence of a dark spell. Maybe she's been hexed to do this to Hermione. In the fanfiction world, this could be a lead - up to a rescue mission by Harry and Ron. They would have to figure out how to break the spell on Fleur and free Hermione.
One possible scenario could be that they are simply having a lazy morning in bed, chatting about their next adventure. For example, Percy might be talking about the latest sea monster he heard about, and Annabeth could be making plans on how to defeat it. Another scenario could be that they are recovering from a battle and finding comfort in each other's presence in bed.
One possibility is that they are forced to share a bed due to some magical or dangerous situation. Maybe they are in a strange place where there is only one bed available as shelter from a threat. They start off awkwardly but gradually learn to respect each other more during the night.
Well, it could be a story about a prank. Maybe Tanya and Bella are friends in the GP (Guiding Principle? Group? It's not clear) universe. Tanya tied Bella to the bed as a silly prank, and then the story could be about how Bella gets revenge or how they both end up laughing about it in the end.
In some cases, it might be a romantic - themed fanfiction where the 'tied to bed' situation is more about a consensual, kinky aspect of a relationship. However, this should always be within the boundaries of appropriate and consensual behavior in the fictional world. But this is just a small part of the many possible interpretations in fanfiction.