In fanfiction, it could be related to a love - hate relationship. Maybe Draco has a love interest who is angry with him. So, in a fit of rage, they use a spell to drag him behind them. Or it could be part of a magical duel where he loses and is then dragged behind the victor as a sign of defeat. Another idea is that he's being dragged behind in a quest or adventure where he's not fully on board, but others are making him participate by force.
One possibility could be that Draco is being forced into a situation against his will. Maybe he's being dragged behind in a magical chase where his enemies are after him, and his friends or foes are pulling him along as they flee or pursue. It could also be part of a prank gone wrong in the wizarding world, where he ends up being dragged behind someone's magical transportation device.
Well, perhaps in the fanfiction, Draco has been caught up in some dark magic plot. He might be dragged behind as a captive, being taken to a secret location. The ones dragging him could be dark wizards or witches who have plans for him, either to use him as a pawn in their evil schemes or to extract some sort of information from him. It could also be a situation where he's being punished by his own Slytherin peers for some misdeed, and they are literally dragging him behind them as a form of humiliation.