Percy could cope by relying on his friends. His friends are very resourceful and they would surely help him out. They could carry him around when needed and be his eyes and ears in dangerous situations.
Percy could also cope by finding new meaning in his situation. He could become an inspiration for other disabled demigods or humans. He might start a support group or something similar. He could also use his situation to raise awareness about the importance of helping those with disabilities in the demigod world. He would have to go through a process of acceptance first, but once he does, he could make a real difference.
Well, they could rely on their friends a great deal. Just like Percy has his friends at Camp Half - Blood. They could help with things like getting around, getting food, and protection. His friends might also try to find a cure or at least some way to make the paralysis less severe.
In the 'Percy Jackson Gets Paralyzed' fanfic, his relationships with other characters would surely change. His friends would probably be more protective of him. Percy himself might go through a period of depression at first, but then he'd start to adapt. He could become a strategist for the demigod team, using his knowledge of monsters and his past experiences to guide others in combat, even if he can't fight physically as he used to.
A simple way would be through their powers. Harry sees Percy's instant and powerful control over water, while his own magic related to water is much more limited. This makes him envious.
One idea could be that Percy is paralyzed during a battle with a new and powerful monster. His friends then have to find a way to heal him while also protecting him from further attacks. Maybe they seek the help of a god who is known for healing but has a difficult task for them in return.
Perhaps Percy would try to understand the primordial's reasons for the betrayal. He's a smart and empathetic character. He might think that there was some misunderstanding or that the primordial was forced into it. So, instead of immediately retaliating, he could try to communicate with the primordial to clear things up. If that doesn't work, then he would be more likely to take a defensive stance rather than an offensive one, at least until he fully understands the situation.
At first, Percy would probably be angry and frustrated. Losing an eye is a huge deal. But he's also a determined person. He would start to practice with his remaining senses more intensively. He'd learn to listen more carefully for approaching enemies, feel the vibrations in the ground or water more acutely. He might also seek out some magical or medical help within the demigod world. There could be potions or spells that might help him either regain some vision or enhance his other senses to make up for the loss.
One popular fanfic idea could be Percy being summoned to a modern-day high school. In this fanfic, he might be summoned by a group of students who accidentally stumble upon an ancient spell. Percy then has to deal with the normal high school problems like bullies and exams, all while trying to keep his demigod identity a secret.
One way could be that it's a gift from a minor god. Maybe a god associated with fire secretly blessed Percy, giving him this power.
In a fanfiction context, Percy Jackson could avoid being hunted by the Avengers by using his knowledge of the magical world. He could seek help from other demigods or even some friendly gods. Maybe they could create a diversion or put a spell on the Avengers to make them forget about Percy. Also, Percy could try to blend in with the normal humans. Since he's half - human, he could act like an ordinary person and not draw attention to himself. But this would be difficult as his powers sometimes act on their own.
Percy would probably rely on his friends. In the Percy Jackson series, his friends were always there for him. In this fanfiction situation, he'd need them more than ever. They could help him stay grounded and remind him of his true self, not the dark legacy of Voldemort. Also, he might learn more about his demigod side to overpower the dark side in him.