One interesting plotline could be Harry learning the pure - blood traditions from the Malfoys in a different way than he expected. He might gain a new perspective on the wizarding world's social hierarchy.
Well, it could be a total chaos. Harry's values are so different from the Malfoys'. He might constantly clash with Draco and Lucius. But on the other hand, it could also lead to some interesting character developments. Maybe Harry could gradually change the Malfoys' views on Muggle - borns over time.
His relationship with Draco could force him to be more empathetic. Instead of just seeing Draco as an enemy, he has to live with him daily. This could lead to Harry developing a more nuanced understanding of people, and his character could become more forgiving and less impulsive in his judgments.
It would be very strained at first. The Malfoys would see Harry as an intruder and a symbol of what they oppose. But as time goes on, they might start to see his good qualities. Harry, for his part, would always be on guard but might also feel a bit of pity for them as he learns more about their insecurities.
The Malfoys could save Harry in fanfiction because of a personal debt. Maybe Harry once unknowingly did something that benefited the Malfoys greatly. This could be as simple as preventing a disaster from befalling their family business or saving the life of a family member secretly. When the time comes, the Malfoys feel obliged to return the favor and save Harry from whatever danger he is in. Also, it could be part of a complex plot where the Malfoys are trying to redeem themselves, and saving Harry is a big step in that direction.
In Harry Potter fanfiction, the Malfoys are often portrayed in a more complex and sometimes positive light. Some fanfictions might explore Draco Malfoy's struggle between his family's beliefs and his own emerging sense of right and wrong. He could be shown as having a change of heart, perhaps influenced by his interactions with Harry and his friends. This gives a new dimension to his character that we don't fully see in the original books.
It could also be a part of a plot by the Malfoys to gain influence. They know Harry is a well - known figure in the wizarding world. By calling him and interacting with him, they might hope to improve their public image or gain some political leverage within the wizarding community.
In fanfiction, their relationship can be complex. Sometimes they might be forced to work together against a common dark threat. For example, in some stories, a new dark wizard arises who is more powerful than Voldemort, and both Harry Potter and the Malfoys have to put aside their differences to stop this new evil. It could also involve a change in Draco Malfoy's character, where he starts to see Harry in a different light and they form an uneasy alliance.
In the 'Harry adopted by the Malfoys' fanfiction, one possibility is that Harry would receive a very different kind of magical education. The Malfoys might try to mold him into a Slytherin - like wizard, but Harry's own Gryffindor - like courage would constantly be at odds with that. Also, his relationship with Draco could be very complex, ranging from initial rivalry as they are brought up in the same household to a possible understanding and even friendship later on.
Well, in such a fanfiction, Harry might be given a very different education. The Malfoys could try to indoctrinate him with pure - blood supremacist ideas at first. But as he grows, he might rebel against it. He could also be exposed to a different social circle within the wizarding world. Maybe he would have more interactions with other Slytherin families and this would change how he views things like House rivalries. And his relationship with Dumbledore would be very strained as the Malfoys are not on good terms with Dumbledore.