One possible plot point could be Voldemort's change of heart. Maybe seeing Harry being abused makes him question his long - held enmity towards Harry. He might start to see Harry as more of a victim than an enemy, which could lead to some really strange alliances or at least a change in his approach towards Harry.
In this type of fanfiction, a plot point could be that Voldemort witnesses the abuse and it stirs up memories of his own difficult past, if we assume he had one. This could create a strange connection between him and Harry. He might then take it upon himself to 'protect' Harry in his own twisted way, which would be very different from his normal behavior. This could also cause a stir in the wizarding world as everyone tries to figure out Voldemort's motives for getting involved in Harry's situation.
Well, perhaps in this fanfiction, Voldemort decides to use the situation of Harry being abused to his advantage. He could try to manipulate Harry, thinking that a broken and abused Harry would be easier to control. Or, on the other hand, he might feel some sort of pity that he doesn't quite understand, and this could lead to internal conflict within Voldemort as he struggles with his dark nature and this new - found feeling.
One possible interesting plot point could be Harry's internal struggle. On one hand, he has been raised in an abusive situation, and on the other, he discovers this shocking relation to Voldemort. He might struggle with his own identity and whether he has the potential for evil within him like his supposed father.
In this fanfiction, Voldemort's character is explored in a way that challenges our traditional view of him. His seeing Harry abused might make him reevaluate his relationship with Harry. He may start to see Harry not just as the Boy Who Lived who he wants to defeat, but as a person who has suffered, much like he might have in his own way. Harry, on the other hand, is stripped of some of his heroic facade. His abuse makes him more relatable in a sense. We can see his pain and how it affects his actions and decisions, and also how he reacts to Voldemort's new - found interest in his situation.
One plot idea could be that Voldemort saves Harry from his abusers in the Dursley household because he realizes Harry's potential is being squandered there. He then takes Harry under his wing, not to turn him evil, but to train him in magic in a very different way than Hogwarts. Maybe he wants to use Harry as a tool against the Ministry, which he believes is corrupt.
One possible plot point could be the discovery of this relationship. Maybe Harry finds some hidden magical artifact or document that reveals the truth. Another could be the reaction of the wizarding world. Would they still see Harry as a hero or would they be suspicious of him? Also, Voldemort's reaction if he were to find out before his death could be interesting. He might try to use Harry for his own ends in a different way than in the original story.
One plot point could be Percy using his powers to protect Harry from his abusers. For example, he could create a water shield around Harry when his abusers try to harm him. Another could be Harry teaching Percy some of the magic he knows in return for the protection. This exchange of skills between the two different universes would be really cool.
One common plot point is Harry's disillusionment with the wizarding world. Maybe he feels betrayed or mistreated, which leads him to turn to dark magic and revive Voldemort as a form of revenge.
Yes, there are some fanfictions with this concept. It's an interesting take on the Harry Potter universe as it flips the typical relationship between Harry and Voldemort. In these fanfictions, the story often explores how Voldemort's actions change when he takes on the role of an adoptive figure to Harry, who has been abused. It can lead to some really unique character developments and plot twists.
One interesting plot point could be that Harry discovers a hidden agenda of Voldemort that was unknown to everyone. Maybe there was a part of Voldemort's plan that was so well - hidden that only by having his memories can Harry find out. This could lead to a new race against time to stop something that Voldemort had set in motion long ago.
There are quite a few plot points that could be explored. For instance, the graveyard could be a place where the magic of the dead has an effect on both Harry and Voldemort. It could make Voldemort more vulnerable in some ways, and Harry could use this to his advantage, not for a fight but to try and change Voldemort. Or perhaps there is a hidden prophecy in the graveyard that only they can uncover together. This would force them to cooperate, at least for a while. Also, the idea of Harry using the knowledge of the graveyard's history (maybe it was once a place of great magic before it became a dark place) to outwit Voldemort. It would be a battle of wits rather than a physical or inappropriate encounter as in lemon fanfiction.
One popular one might be 'Voldemort's New Heir' where Voldemort discovers Harry's abused situation and decides to take him in for his own purposes. He starts to train Harry in dark magic, but an unexpected bond forms between them.