It could be that Naruto discovers something about the nature of his pregnancy that scares him. For example, he might find out that the child has some sort of special power that could put it in danger. So he runs away to figure out how to handle the situation without endangering the village or the child. He might seek out a hermit or an old sage to get advice on what to do.
Perhaps Naruto is running away from a relationship that has gone wrong. He got pregnant, but the father of the child has turned out to be someone untrustworthy or dangerous. Naruto, being the protective person he is, decides to run away to start a new life for himself and his unborn child. He could end up in a small, hidden village where he tries to build a new life while hiding his true identity.
Another direction the fanfiction could take is that Ginny gives birth in secrecy. The birth could be a magical and life - changing experience for her. After that, she might raise her child in hiding for a while, teaching the child all about the wizarding world in her own unique way. Eventually, when the time is right, she could re - enter the wizarding society with her child, causing a stir and a lot of questions from everyone around her.
Well, he might encounter some unique Kiri ninjas. Maybe he'll meet someone who becomes his unexpected ally. For example, a young and idealistic Kiri ninja who is also a bit of an outcast in their village. They could bond over their shared feelings of not fully fitting in.
Well, Naruto might run away with Itachi's ideals or some memento of Itachi. Maybe he uses it to become stronger and face new enemies. He could also be on a journey to uncover more secrets about Itachi that no one else knows.
It could also be due to a sense of confusion. Naruto suddenly finds himself in this unexpected situation. He doesn't know how to deal with it and feels that running away is the easiest way at the moment to escape from all the chaos and figure things out on his own.
He might face many challenges on his way. In the desert, he could struggle with the harsh environment, like finding water and shelter. Also, he may encounter some Sand Ninja who might be suspicious of him. Maybe he'll meet Gaara and they'll form an unexpected bond, as they both have had difficult childhoods.
Perhaps he'll find a hidden place where he discovers ancient jutsu. This could be a turning point for him to become stronger on his own terms, away from the neglect of his family.
One possibility could be that Stiles runs away because he's afraid of the reactions from his friends and family. Maybe he thinks they'll be disappointed or angry. He might go to a place where no one knows him to start a new life for himself and his unborn child.
In this fanfiction, it could be that Lucy is part of a society with strict rules about pregnancy out of wedlock. She runs away pregnant to avoid the shame and punishment that would come her way. As she runs, she might meet other outcasts who support her. She then has to figure out how to survive, find medical care for her pregnancy, and create a future for herself and her baby.
Well, perhaps Kagome runs away because she's pregnant and fears the reaction of her family or friends. Maybe she wants to protect the unborn child from some sort of danger or judgment in her original community.
He might meet an old hermit who teaches him a unique and powerful jutsu that his family never knew. This new jutsu gives him an edge and also makes him more confident in his abilities. He could then use this newfound power to help those in need, all while staying away from his family.