In a fanfiction like this, it might also be that Grimmjow has been influenced by some outside force. For example, a new, powerful enemy might be manipulating Grimmjow to kidnap Ichigo. Grimmjow, being prideful and not one to be pushed around easily, may initially resist but then sees an opportunity to prove his strength by taking on Ichigo in this new situation. And so, he kidnaps Ichigo. The story could then focus on Ichigo trying to figure out why Grimmjow is doing this and how to escape.
Well, one possibility could be that Grimmjow has some personal vendetta against Ichigo. Maybe he wants to use Ichigo as a bargaining chip with the Soul Society. He could be tired of Ichigo always getting in his way during battles and decides to take him to a secluded location where he can deal with him on his own terms.
Rukia would be extremely worried. She would likely try to gather her friends in the Soul Society and form a rescue party. She has a strong bond with Ichigo and would not stand by while he is in danger. She might also be a bit angry at herself for not being able to protect Ichigo in the first place.
In the 'ichigo is grimmjow's pet fanfiction', it could start with Grimmjow capturing Ichigo during one of their intense battles. Grimmjow sees Ichigo as a unique find and decides to keep him around instead of killing him. He puts Ichigo in a situation where Ichigo has limited freedom and has to rely on Grimmjow for basic necessities. As time passes, Ichigo tries to break free from this pet - like status, but also starts to understand Grimmjow's past and the reasons behind his aggressive behavior. This new understanding might lead to a change in their relationship, from a captor - pet dynamic to something more complex and perhaps even an alliance against common enemies.
One possible plot could be that Ichigo kidnaps Rukia out of a desperate need to protect her from some unseen and extremely dangerous threat in the Soul Society. He might believe that the Soul Society's own mechanisms for safeguarding her are insufficient.
One possible plot twist could be that Aizen has a hidden motive other than just causing chaos. Maybe he kidnaps Ichigo to use his unique powers for some sort of experiment. For example, he might want to extract the power of Ichigo's Hollow side to enhance his own strength or create a new type of Arrancar. Another twist could be that Aizen is being controlled by an even greater force, and Ichigo's kidnapping is part of a larger plan to draw out other powerful characters in the Soul Society.
Some possible titles could be 'Female Ichigo's Encounter with Grimmjow', 'The Bond Between Female Ichigo and Grimmjow', 'Female Ichigo and Grimmjow: An Unlikely Pair'.
At the start, Ichigo would be defiant. He would not show any fear in front of Aizen. He might taunt Aizen, trying to get him to reveal his true intentions. As time goes on, he would start to feel a sense of isolation, but this would only strengthen his resolve. He would use his inner Hollow powers more freely, as he has no other option. He would also be constantly thinking about ways to turn the tables on Aizen and escape, and would be ready to take on any challenges that come his way during his captivity.
One idea could be that they are rivals in high school sports, like on the track team. Grimmjow is overly competitive and Ichigo is determined not to let him win all the time. Their rivalry gradually turns into an understanding and then friendship, and maybe more as they discover they have more in common than they thought.
In the manga, Ichigo is known for his spiky black hair and his clothing changes but often incorporates elements of black and red. Grimmjow has distinctive blue hair and usually wears a combat outfit that combines white and black colors.
In the fanfiction, perhaps they are forced to team up due to a common enemy. As they spend time together, they realize they have more in common than they thought. Female Ichigo might be intrigued by Grimmjow's wild nature, and Grimmjow could be attracted to her strength. They could end up having deep conversations about their pasts and their places in the world, and this could lead to a strong emotional bond between them.
The connection between Ichigo and Grimmjow in the manga is one of conflict and a strange kind of connection born from their battles. Grimmjow sees Ichigo as a worthy opponent, and their interactions shape the plot in significant ways.