In some fanfics, this could happen due to a different take on Voldemort's character. Maybe the author wants to explore a redemption arc for Voldemort. He might see something in Harry that makes him change his mind about killing him and instead decides to rescue him from Vernon's bad treatment. It could also be part of a complex plot where Voldemort has ulterior motives that initially seem like a rescue but are actually part of a bigger scheme.
Perhaps Voldemort has a change of heart. He realizes that Harry has some value to him alive other than just being his enemy.
Maybe Voldemort uses his magic to stun Vernon first. Then he could simply apparate with Harry to a safe place.
Well, in some fanfics, Voldemort might have his Death Eaters spying on the Dursleys. So they could've reported Harry's location to him. Another possibility is that Voldemort has some sort of dark magic tracking device on Harry that led him there.
One motive could be that Voldemort wants Harry on his side. He might think that by rescuing Harry from Vernon, who was clearly a bad caretaker, Harry would be more inclined to listen to him and join him.
One scenario could be that Voldemort has a change of heart. He might have had a vision or a revelation that made him realize that Harry is more valuable alive and not under the cruel treatment of Vernon. Another scenario is that Voldemort wants to manipulate Harry. By rescuing him from Vernon, he can start to build a relationship with Harry based on gratitude. This way, he can later persuade Harry to join his side or use Harry's power for his own purposes.
Well, in some fanfiction scenarios, Snape might rescue Harry from Azkaban because he discovers new evidence that clears Harry's name. Maybe he uncovers a dark plot by some other powerful wizard who framed Harry, and his sense of justice, despite his past animosity towards Harry, drives him to act.
In some dark fanfiction scenarios, Vernon might kill Harry Potter out of his extreme hatred and fear of magic. Maybe he discovers Harry's magic in a moment of rage and overreacts, using a weapon or his brute force to end Harry's life. However, this goes completely against the essence of the original series where Vernon was more of a bumbling, non - magical threat.
Well, if Sirius takes Harry to Voldemort in a fanfic, it would be a huge deviation from the normal story. One possibility is that Sirius is trying to make some sort of deal with Voldemort to save others. But Voldemort is not one to be trusted. Harry, being the Boy Who Lived, is a valuable asset to Voldemort for his own dark purposes. It could lead to a tense stand - off where Harry has to use his own wits and magic, even at such a young age, to try and escape the clutches of the Dark Lord.
Another possibility is that it's an accidental result of a powerful magic clash between Voldemort and Harry. When their magic collides in a certain way, it causes an unexpected transformation on Harry, turning him into a girl. This would add a whole new layer of complexity to their relationship and the overall story.
In such a fanfic, one possibility could be that the Armistice is brokered by an unexpected third party. Maybe a powerful magical creature that both Harry Potter and Voldemort respect. This creature could convince Voldemort that the continuous war is only weakening the wizarding world as a whole and that there could be a better way to achieve his goals without all the bloodshed. Harry, on the other hand, would be skeptical but might see it as an opportunity to finally end the war and start rebuilding the wizarding community.