Yes, in many fanfictions, Damon and Elena do get back together. Fanfiction writers often explore their relationship further and give them a second chance at love, as many fans were disappointed when they didn't end up together in the original series.
One success story I know is about a guy named Tom. He realized he took his girlfriend for granted. So, he started by writing her sincere letters, not just asking for forgiveness but also sharing his real feelings. He also made an effort to be part of her interests again. He joined her in volunteer work she loved. In the end, she saw his genuine change and they got back together.
Often, in fanfiction, there's a time - jump scenario. After a period of time apart, both Damon and Elena have grown and changed. Damon has become more self - less, perhaps having worked on his issues with his brother. Elena, on the other hand, has realized that her feelings for Damon were deeper than she thought. They then meet again by chance and start to rekindle their relationship. Another scenario could be that a magical or supernatural event forces them to work together. During this time, they remember all the good times they had and fall back in love.
There was a couple where the guy, Jack, had a fight with his girl over something silly. Jack started to give her space at first. But then he planned a surprise. He invited all their mutual friends and organized a small party. He made a speech there, admitting his wrongdoings and how much he loved her. His girlfriend was touched and they reconciled.
Caroline would probably be really happy. She's always been a big supporter of Stefan and Elena's relationship. She'd be the one planning get - togethers and trying to make sure they have time alone to reconnect.
Annabeth could show her determination by going out of her way to be in the same places as Percy. She'll be wherever he is, whether it's at his favorite spots or events he attends. And she'll always be there with a kind word or a helpful gesture, constantly reminding him of their connection. Also, she might face any danger or difficulty that comes her way while trying to get close to him again, showing that she's willing to do whatever it takes.
A friend of mine, David, had a big fight with his girlfriend and she left. He decided to give her space at first. After a while, he invited her to a special event, a concert of her favorite band. He also apologized sincerely during the event. She was touched by his thoughtfulness and how he respected her space, and they reconciled.