Elena would probably be terrified at first. She's a human in a world full of powerful supernatural beings. Being kidnapped by Damon would mean she's in a very vulnerable position. She might initially try to fight back or escape, using any opportunity that presents itself.
One possible motive could be Damon's possessiveness. In the 'The Vampire Diaries' universe, Damon has a complex relationship with Elena. He might kidnap her out of fear of losing her to someone else, like Stefan. Maybe he thinks that by taking her away, he can have her all to himself and make her see that he is the one she should be with.
Stefan would be extremely worried and angry. As Elena's other love interest, he has a deep connection with her. He would immediately start looking for her, using all his vampire skills and resources. He would probably suspect Damon right away, given their history of rivalry over Elena.
One possible motive could be power. Damon might see Elena as a pawn in his game to gain more influence in the supernatural world. He could think that by kidnapping her, he can control those who care about her and make them do his bidding.
She could be terrified at first. After all, Klaus is a very powerful and dangerous vampire. But Elena is also a strong - willed character. So she might quickly gather her courage and start looking for ways to escape.
The Salvatore brothers, Stefan and Damon, are the most likely candidates. They both have a strong connection to Elena and would stop at nothing to rescue her. Stefan's sense of chivalry and Damon's fierce protectiveness would drive them to track down Katherine and get Elena back.
Elena would likely be angry. She has her own agency and doesn't like being controlled. If Stefan kidnapped her, she would fight back. She might use her knowledge of the supernatural world and her relationships with other characters to try to escape. For example, she could try to call out to Damon telepathically if they have some sort of connection in the story.
I think Stefan can be a really liked character in these fanfictions even though he's in a bit of a love triangle situation. His complex relationship with Damon and his past with Elena make him an interesting addition. He might be shown as still caring for Elena but also coming to terms with her love for Damon. Also, Alaric is a character that many fans like. He can act as a mentor or a voice of reason in the fanfiction, and his relationship with Damon and Elena can be explored in different ways.