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.
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.
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.
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.
I've heard of a fanfic called 'The Blue and the Orange'. In this, the author does a wonderful job of portraying female Ichigo's strength and how it catches Grimmjow's attention. It's set in a post - war scenario where they have to team up against a new threat. It's full of action and also has some sweet moments between the two characters.
Common themes include the struggle for identity. Ichigo is part - Hollow and Grimmjow is an Arrancar, and they both have identity issues to some extent. Fanfics often deal with how they come to terms with who they are. Another theme is the idea of second chances. Given their initial enmity, fanfics might give them a second chance at a relationship, whether it's a friendship or something more complex. And of course, the theme of power - sharing and cooperation, as they learn to use their powers together in some fanfics.
Well, AO3 is probably the best bet. It allows for a wide range of tags and filters which can help you narrow down your search for the exact type of female Grimmjow x Ichigo fanfiction you want. Another place could be Tumblr. There are often fanfiction writers who post snippets or links to their stories there, but it might take a bit more digging to find the full stories.
One popular story could be 'Ichigo's Unexpected Bond with Grimmjow'. In this fic, their relationship develops in a unique way, perhaps starting from a fierce rivalry and gradually turning into something more. It might explore how Ichigo's understanding of Grimmjow deepens over time.