Well, a common theme is the clash of their ideologies within the context of the kidnapping. Ink, who is all about creation, and Error, who is about destruction, are forced to interact closely. This can lead to some really interesting dialogues about the purpose of their existence. Another theme is the role of other characters in response to the kidnapping. Some fanfictions might show how other minor characters react to Ink's disappearance and what they do to find him. And the theme of change is also there. Both Ink and Error could change in some way due to this extreme situation.
A frequent theme is the unexpected bond that might form. Despite the initial hostility of a kidnapping situation, Ink and Error could start to understand each other better. There's also the theme of the setting. The place where Ink is kidnapped to can play a big role. It might be a dark, desolate place representing Error's world, which can add to the overall mood of the fanfiction. And sometimes, the fanfictions explore the concept of redemption. Error might have some form of self - realization during the kidnapping and start to question his actions, especially if Ink has an impact on him.