Harry might use his wits and the environment around him while in captivity. For example, if he's held in a place with magical artifacts, he could use them to his advantage. He could break the chains that bind him with a spell - enhanced object and then make his way to Voldemort and defeat him.
It could be Dumbledore from beyond the grave. He might find a way to reach out and summon Harry, believing that only Harry has the potential to truly defeat Voldemort in this new, dire situation.
Because the Harry Potter series has a huge and passionate fan base. The world J.K. Rowling created is so rich and detailed that fans want to explore different aspects of it through fanfiction. They might want to see different character pairings, new adventures for the characters, or explore what could have happened if certain events in the original series had gone differently.
Maybe Harry uses some powerful and unexpected spells. For example, he could combine the Patronus Charm with a blasting spell. The Patronus might distract Voldemort while the blasting spell hits him hard.
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.
At first, it would be extremely tense and full of suspicion. Harry would be very wary of Voldemort's motives for protecting him. Voldemort, on the other hand, might be impatient with Harry's lack of trust.
It might start with Voldemort's initial curiosity. He realizes Harry is more than just a threat. So he begins to observe Harry closely. As time goes by, Voldemort may start to feel a strange sense of connection, like he's the only one who truly understands Harry's power.
Well, it could be for power. Maybe Voldemort realizes that by saving Harry, he can gain some sort of power over him or use him as a tool in a more elaborate plan.