Often, Dumbledore as Death would be a very complex character. He may not be the straightforward evil or good. His role might be more about maintaining a balance in the wizarding world, which is similar to the concept of Death in some mythologies. He could be using his influence on the different characters in different ways. For instance, his relationship with Snape could be a part of his plan as Death. Snape's actions, which were so crucial in the original story, might be reimagined as being directly or indirectly guided by Dumbledore - as - Death. This could add a whole new layer of mystery and intrigue to the fanfiction.
One key plot point could be Dumbledore's true identity being revealed gradually. Maybe Harry starts noticing strange things about Dumbledore that make him suspect he is not just an ordinary wizard but Death itself. Another could be how the prophecy about Harry and Voldemort fits into this new paradigm where Dumbledore is Death. It might change the meaning of the prophecy completely, as Dumbledore - as - Death could have a different intention behind the events related to the prophecy.
It's a really horrible idea. In the original 'Harry Potter' series, Dumbledore is like a father figure to Harry. Their relationship is based on trust, guidance and mutual respect. This idea completely subverts the positive image and relationship established in the original work.
I haven't come across such a disturbing fanfiction myself. In the official 'Harry Potter' lore, Harry and Dumbledore have a mentor - mentee relationship and there's no such violent scenario. Fanfiction that goes against the core values of the original work like this is not only untrue to the spirit but also quite abnormal.
There's also a chance that Dumbledore gets caught by a group of rogue magical creatures. For instance, if he was exploring an area that was supposed to be off - limits to wizards and the creatures there saw him as an intruder. They might not be as rational as wizards and could hold him captive without really understanding who he is.
Well, it could be that Dumbledore has some sort of hidden device or spell that he activates when kidnapped. For example, he could have a charmed object that sends a signal to his allies, like the Order of the Phoenix. His allies then come to his rescue and he manages to escape during the chaos. Also, Dumbledore is extremely intelligent. He might outwit Grindelwald by engaging him in a complex conversation full of riddles and misdirections, which gives him an opportunity to break free.
It could be Severus Snape. He has a complex relationship with Dumbledore. Maybe Snape discovers some of Dumbledore's plans that he doesn't agree with regarding Harry Potter. He then sends a Howler in a fit of anger to express his disapproval.
In a fanfiction, Dumbledore might steal out of desperation. Suppose there was a situation where a curse was about to be unleashed on Hogwarts, and the only way to stop it was by stealing a particular ingredient for an antidote from a place where it was not supposed to be taken. Dumbledore, seeing no other option, decides to steal it. His motive here is to save the school and its students, even if it means breaking the rules.
Fred and George Weasley are very likely candidates. They are known for their love of pranks and their mischievous nature. They might see pranking Dumbledore as the ultimate challenge.
Dumbledore, as Harry's guardian in the fanfiction, would probably use his influence in the wizarding world. He could make sure that Harry is taught by the best teachers at Hogwarts. He'd also be there to offer advice and guidance, especially when Harry faces challenges like dealing with Voldemort or other dark forces. For example, he might teach Harry some advanced defensive magic privately to better protect himself.