It could be an older brother. He's home alone with his younger siblings. He has to take on the role of a parent for a while. He makes sure they are fed, bathed, and entertained. He also has to deal with any problems that come up, like a broken toy or a fight between the younger kids. It's a story about his growth and responsibility.
The main character could be a mischievous little boy. He's always getting into small troubles around the house when his family is there. So when he's home alone, he really has a field day. He might try to build a huge fort in the living room or attempt to cook something really elaborate but ends up making a big mess.
Perhaps the main character is a boy named Sam. Sam is a bit of a troublemaker usually, but being home alone changes him. He realizes the importance of responsibility. He has to take care of his pet dog while his parents are away. And when some unexpected events happen, like a small fire in the kitchen because he tried to cook something fancy, he learns from his mistakes and becomes more mature in the process of dealing with these situations.
Maybe it's a young adult who has moved to the big city for work but always looks forward to going back to their small - town home for Christmas. They might have to deal with the hustle and bustle of city life and then find peace and comfort when they return to their family's place.
The main villain could be an escaped criminal who stumbles upon the house thinking it would be a good place to hide. But when he realizes there's a kid alone, he decides to take advantage and ransack the place. The kid has to use his wits and the resources around the house to defeat this dangerous villain.
It could be a rogue wizard who has a vendetta against the Dursleys for some reason and decides to attack when Harry is home alone. Maybe the Dursleys once unknowingly wronged this wizard's family, and he wants revenge.
It could be a young lesbian just coming to terms with her sexuality. She might have been struggling in a conservative family or school environment where she felt like an outcast, but then she found a mentor or an older lesbian who guided her and made her feel that she was not alone.
It could be a young adventurer who decides to explore an abandoned house at night.
The main character is the girl who walks home alone at night, though without more context about the specific novel, I can't give more details about her.
Since I don't know the exact 'home alone novel', I can't say for sure. But it could be a young boy or girl as the main character, perhaps with some neighbors or family friends who play important roles.
Perhaps in this fanfiction, Kevin discovers a magical ability while being alone in New York. He can communicate with the pigeons, and they become his allies. The '967' could be some sort of frequency or signal that only he and the pigeons can understand, which helps him in his new adventure against the bad guys.
It could be a lost traveler. Someone who got separated from their group while on an adventure or a journey.