The characters' reactions would vary. Those who are more open - minded might enjoy seeing new takes on their lives and relationships. However, more traditional characters might be resistant to changes made in the fanfiction. They might feel that their true nature is being distorted, especially if the fanfiction contains elements that are completely contrary to their original traits.
They could be either delighted or disappointed. If the fanfiction captures their essence well and tells an interesting story, they would be happy. But if it misrepresents them, they would be unhappy. For example, a heroic character made into a villain in the fanfiction would not be happy.
Some characters may be flattered by the attention and the creative interpretations in the fanfiction.