One reason could be burnout. After years of facing dangerous and often terrifying situations, Dean might just be too exhausted to continue. Hunting has taken a toll on his mental and physical health, so he decides to step away.
In some fanfictions, when Dean leaves hunting, he might try to lead a normal life. He could focus on building relationships, like getting closer to his family or starting a romantic relationship. He might also explore new hobbies or get involved in community activities, far away from the world of the supernatural.
Well, in some fanfictions, Dean might throw away the amulet because it represents a past he wants to leave behind. Maybe it's tied to a lot of pain and loss, and getting rid of it is a way for him to move forward. It could also be that he feels like the amulet has lost its significance in his new journey, so he just discards it.
Hermione could leave Draco if she realizes that they have fundamental differences in values. For example, if Draco still holds some pure - blood supremacist views, Hermione, being a Muggle - born advocate, would not be able to tolerate it in the long run.
Well, it could be for love. In many fanfics, their relationship has been through a lot, and leaving together is a way to start anew, away from the prying eyes and pressures of Hogwarts and the wizarding community.
Dean would become more protective. His tough - guy exterior would soften as he takes care of the baby. He'd be more cautious in his hunts, not wanting to leave the baby unprotected.
Perhaps he's following a lead related to his parents. There could be some secrets about his family that are hidden in America. He goes there to uncover the truth and learn more about his family's past that might not be available in the UK.
One reason could be that he's on a mission to find other heroes in the universe. He believes that Earth needs more allies in case of future threats. So he leaves Earth to search for powerful beings or civilizations that could potentially help protect Earth. He embarks on this journey alone, relying on his Iron Man technology and his wits to survive the perils of space travel.
They could leave because of a prophecy. Some ancient prophecy might state that they need to leave Konoha to fulfill a greater destiny elsewhere. So they trust in this prophecy and leave their home.
Dean would probably be very protective. He's always been the big brother looking out for Sam, and with Sam as a kid, that instinct would be even stronger. He'd be constantly worried about Sam getting hurt and would keep him close at all times.
They might be really surprised. Some fanfictions could show them in situations they never thought of. For example, if there's a fanfic about them having a normal life for a while, away from hunting, they could be both amused and a bit bewildered.