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 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.
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.
One possible story could be that mom discovers some illegal activity by a group of people. They blackmail her to keep silent by tying her to the bed and threatening to harm the family if she tells anyone. However, mom manages to leave some clues for the family to figure out what's going on.
One possible story could be a prank gone wrong. Maybe the husband was trying to play a harmless joke on his wife, like a pretend 'kidnapping' scenario for fun. But then things got out of hand when she couldn't easily free herself and they both ended up having a big laugh about it once she was untied.
One possibility could be that it's part of a prank gone wrong. Maybe Annabeth was trying to play a practical joke on Percy and tied him up, but then things start to spiral as they face some unexpected danger while he's tied. And they have to figure out how to get Percy free and deal with the situation together.
One possible plot could be that it's a prank gone wrong. Maybe some magical spell misfires and Harry ends up tied to Snape's bed accidentally. Then Snape discovers him and there is a lot of anger and confusion as they try to figure out how to undo the situation without getting into more trouble.
One possible plot could be that it's part of a prank by the kids. They might be playing a game like 'hostage' and they use soft ropes or scarves to tie mom to the bed in a pretend scenario, and then they have to negotiate with dad or other family members to 'free' her.