In certain fanfiction works, Tatsumi is indeed made into Esdeath's pet. This can be a way for writers to explore darker or more extreme versions of their relationship. It might involve Esdeath treating Tatsumi in a demeaning way at times, or it could also lead to a strange form of affection developing between them as the story progresses. It really varies from one fanfic to another.
You can try looking on some fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfics, and you might be able to find Esdeath and Tatsumi - related ones there. However, make sure to follow the site's rules and regulations.
Tatsumi might also face opposition from his friends and allies. They would likely be very suspicious of Esdeath and not understand why Tatsumi is falling for her. His friends could try to convince him that she's not good for him, which would put a strain on his relationships with them as well as his new - found feelings for Esdeath.
The popularity might stem from the complex relationship between Esdeath and Tatsumi in the original 'Akame ga Kill!' anime. Their dynamic, with Esdeath being a powerful and somewhat cruel character and Tatsumi being the more idealistic hero, creates an interesting contrast that fanfic writers like to explore further in a romantic or more adult - themed context (while still keeping it within the boundaries of fanfiction).
If Tatsumi is Esdeath's pet in fanfiction, there could be a storyline where Tatsumi is forced to participate in Esdeath's cruel games. He might be made to fight other 'pets' or perform dangerous tasks for her amusement. Or, perhaps Tatsumi tries to use his position as her pet to gain information and eventually turn the tables on Esdeath, leading to a plot full of intrigue and suspense.
In this fanfiction, the development of their relationship would be full of twists and turns. Esdeath is used to getting her way, but Tatsumi won't just submit. This would lead to some initial clashes. However, as they face difficulties together, like threats from other villains or problems within their community, they would realize how much they need each other. Esdeath would start to value Tatsumi's ideals more, and Tatsumi would see the good in Esdeath's loyalty. Their relationship would grow from a forced union in some ways to a deep and loving bond.
In a fanfiction where Esdeath and Tatsumi are married, their life could be full of interesting dynamics. Esdeath, with her powerful and often cruel nature, would have to adjust to a more domestic life. Tatsumi, on the other hand, would need to deal with Esdeath's strong personality. Maybe they would have adventures together, with Esdeath using her skills to protect Tatsumi and Tatsumi teaching her about the value of life and kindness. Their relationship could be a mix of love and conflict as they come from very different backgrounds.
In 'Akame ga Kill', Tatsumi and Esdeath's relationship is complex. Esdeath falls deeply in love with Tatsumi. However, Tatsumi is on the side opposing Esdeath's cruel ways. Esdeath's love is intense but possessive. She tries to make Tatsumi hers, but Tatsumi is committed to his comrades and the revolution. Their love story is tragic as they are on opposite sides of a great conflict.
In a fanfic like this, perhaps there could be a situation where Tatsumi and Esdeath are forced to work together on a mission. During this time, they have to rely on each other and Tatsumi starts to admire Esdeath's strength and leadership skills. These qualities, along with her beauty, might draw him in and make him realize his love for her.
Tatsumi doesn't really welcome Esdeath's love. He sees her as an enemy due to her actions in the empire. Her brutal ways and her role in oppressing the people are things Tatsumi is fighting against, so he can't return her feelings of love.