Well, he might be captured by some Earth - based villains. Maybe S.H.I.E.L.D. mistakes him for a threat and holds him. They could try to study his alien technology and powers.
Perhaps a powerful and secret organization on Earth captures Star Lord. They could be after the Infinity Stones that he has some knowledge of. He might be locked in a high - security facility. During his captivity, he could befriend some Earthlings who help him escape. Or he could use his wits and charm to manipulate his captors into letting him go.
In the fanfic, if Star Lord is captured on Earth, it could lead to all sorts of interesting scenarios. For instance, his fellow Guardians of the Galaxy might come to rescue him. But they would have to deal with Earth's defenses and heroes. Earth heroes could either help or hinder the rescue depending on how they view Star Lord. Also, the captors might try to use Star Lord to get access to valuable information about the outer space and other galaxies. There could be a great power struggle as different parties on Earth try to gain control over him.
In such a fanfic, there could be epic battles. The Empire's advanced weaponry like the Death Star might be used against Earth's defenses. Maybe the Rebel Alliance would also get involved, teaming up with Earth's forces to fight the common enemy.
It could be a powerful alien - hunting group on Earth. They see Star Lord as an alien threat and decide to capture him.
In such a fanfic, Star Lord might be abducted by an alien race. They could be after his unique skills or the technology he has access to. For example, the Skrulls might want to use his knowledge of the Guardians' ship to improve their own fleet.
In such a fanfic, Naruto might be subjected to various interrogations by Kumo. They could be interested in his Nine - Tails power. Maybe they would try to extract information about Konoha's secrets through him.
In a 'Naruto Captured by Akatsuki' fanfic, Naruto might be tortured for information about the Nine - Tails. The Akatsuki are known for their ruthless ways to extract tailed - beast power. They could try to break his spirit and make him cooperate.
Well, in such a fanfic, Harry might be subjected to various interrogations by Abstergo. They could be trying to extract some sort of special knowledge or power from him.
In this fanfic, Katniss might face intense torture. The Capitol is known for its cruelty. They could use various methods to break her spirit, like starving her or subjecting her to mind - games. Maybe they'll try to use her as a tool to control the rebels, threatening to kill her if the rebellion doesn't stop.
Ezra could be tortured for information about the Rebellion. The Empire would be eager to know Rebel plans and bases. His capture might also lead to the discovery of some of the Rebels' secrets if he accidentally reveals something under duress.
In such a fanfic, Harry might be tortured for information about the Order of the Phoenix. Voldemort could try to turn Harry to the dark side, using his powerful magic to break Harry's will.
If the Joker is captured by Batman in the fanfic, Batman could use this opportunity to study the Joker more closely. He might try to understand what really makes the Joker tick, his origin, and his motives in a deeper way. However, the Joker might be planning an escape even while being held captive. He could be using his time in captivity to set up a grander scheme that would put Gotham in even more danger once he breaks free, all while constantly playing mind games with Batman.