They're popular because it's a very relatable concept. Many people have had a crush on someone and felt that sense of obsession at some point. It's also a bit of a fantasy for some, seeing someone be so dedicated to another person.
Perhaps the obsessed guy has a change of heart. He realizes his actions are wrong and lets the girl go. But this ending often comes with a complex set of emotions and consequences for both characters as they try to make sense of what has happened.
Well, often in these stories, the guy starts as a bit of a stalker - not in a creepy way though. He'll find out her daily routine and 'accidentally' bump into her a lot. Then there's the plot where he saves the girl from some sort of trouble, which makes her see him in a new light. Also, there's the scenario where the guy writes her love letters or poems to express his obsession in a more romantic way.
Often, the theme of rescue is present. It could be the girl trying to rescue herself or her friends and family attempting to rescue her. Also, there can be a theme of psychological manipulation as the obsessed guy may use various tactics to control the girl.
The contrast is appealing. It goes against the traditional gender roles. In normal stories, guys are often seen as the dominant ones. So, when an anime girl is in the dominant role, it's fresh and interesting.
Another theme can be self - discovery. Through the process of drawing the girl, the guy might learn more about himself, his feelings, and his artistic style. It could be a journey of understanding his own identity as an artist and as a person in relation to the girl he is drawing.
One common theme is the breaking of gender norms. In these stories, the anime girl defies the traditional expectation that the guy should be in control. For example, in 'Fullmetal Alchemist', Winry Rockbell is a skilled mechanic. She doesn't let the male alchemists around her overshadow her skills and knowledge, and she often stands her ground when it comes to decisions related to her work, which is a form of domination in a sense.
Another anime is 'The Garden of Words'. Here, the male protagonist Takao Akizuki, who is an aspiring shoemaker, often sketches in the garden where he meets Yukari Yukino. His sketches are influenced by her presence and their interactions, and it has a very poignant and artistic feel.
For this fanfiction, first, describe the setting of the auction. It could be a grand, yet seedy affair with all kinds of strange characters. The slave girl, with her big, sad eyes and timid demeanor, catches the guy's attention. He outbids everyone else. Once he has her, he takes her to his home. At first, she is scared, but gradually, she starts to show her true personality. She might be feisty and strong - willed. This surprises the guy, and he begins to respect her. Eventually, they could team up against the corrupt system that allows the auction of slaves in the first place.
One possible plot is that the guy in the van is actually under the control of a more powerful villain. The anime girl, who might be a key figure in the anime's lore, is kidnapped to be used as a bargaining chip. However, during her captivity, she befriends a small creature or another captive in the van. Together, they come up with a plan to escape and expose the real villain behind the kidnapping.