It's not likely that the actual Olympus (in the context of the Percy Jackson series being a place of the gods) reads fanfiction. Fanfiction is a creation of the fans in our world, and there's no indication in the books that the gods or Olympus as an entity would engage with it.
Well, in the world of fanfiction, anything can happen. Regarding Percy Jackson dying in Blood of Olympus fanfiction, there are many fanfictions out there with all kinds of scenarios. Some writers might kill off Percy to explore themes like sacrifice, the impact on other characters, or to create a really dark and dramatic storyline. However, the original series doesn't have this happen, so it's all about the creativity of the fanfic authors.
One possible reason could be that Percy feels betrayed by the Olympians first. Maybe he discovers some dark secrets about them that make him lose faith. For example, if he finds out that they have been using demigods unfairly in their battles or politics.
If Olympus read Percy Jackson fanfiction, the gods might be either amused or offended. Some fanfictions might portray them in a way that they don't like, and they could potentially take revenge on the author (if they could reach our world). But on the other hand, they might find some of the creative interpretations quite funny.
One key element could be Percy's use of his water - based powers in a unique way. Maybe he creates a huge tidal wave to disrupt Kronos' forces. Another element might be his alliances. He could team up with his friends from Camp Half - Blood, and they all use their combined skills to outwit Kronos.
Ares could be a likely character. He's always been somewhat of a wild card in the Percy Jackson series. He might betray Percy for his own amusement or to gain more influence in Olympus. Another could be Zeus. He's often paranoid about his power and might see Percy as a threat and betray him to protect his throne.
One common plotline is Percy finding out that the Olympians have been using him all along. For example, they might have sent him on dangerous quests not just to save the world but also to gain more power for themselves. Another could be Percy being betrayed by a close friend or ally who is working for the Olympians' self - serving plans. Maybe they set him up to take the fall for something he didn't do.
One possible reason could be to create a tragic story. Writers might want to show how the world of the story would be affected by the loss of such a central character like Percy.
Percy himself is always interesting. In fanfiction related to The Staff of Olympus, he might have new challenges and growth. Another is Annabeth. Her intelligence could be used in unique ways to figure out the mysteries of the staff. Grover can also be really cool as he might use his nature - related powers in unexpected ways in relation to the staff.
In fanfiction, if Percy Jackson takes over Olympus, he might bring a new order. He could reform the archaic rules of the gods. For example, he might ensure fairer treatment of demigods, like better training and protection. Also, he could change the power dynamics among the gods, making them more accountable for their actions.