She changes it a great deal. For starters, the gender difference can bring in a new type of relationship. Instead of the more traditional male - male rivalry, there could be an element of attraction or different kind of respect. Also, her way of handling the Force and Jedi teachings might be different, which would affect how Vader reacts to her.
One interesting idea could be a female Obi - Wan being a mentor to a younger generation in a different way than the male Obi - Wan. She might use her unique perspective to train Jedi. As for Vader, a fanfiction could explore his relationship with this female Obi - Wan in a more complex way, like they have a grudging respect for each other's skills.
One possible plot could be that Vader, without his suit, is found by Obi - Wan in a hidden location. Obi - Wan, despite their past, decides to help Vader recover. As they interact, they start to understand each other's perspectives better. Maybe they even form an uneasy alliance against a new common enemy in the galaxy.
Their relationship might start with suspicion. Obi - Wan would be cautious as he's seen Vader's evil deeds. But as Vader is suitless and perhaps more 'human' in a sense, Obi - Wan could start to see the Anakin he once knew. This could lead to a slow rebuilding of trust.
There may not be mainstream, widely - publicized fanfictions with Obi - Wan gagged. But some independent writers might have created stories around this concept. It could be that in a story, Obi - Wan is gagged during a diplomatic mission turned hostile. His captors want to silence him to gain an advantage in negotiations. This could lead to a complex plot where his friends have to use their wits and skills to free him and resolve the diplomatic crisis.
In the fanfiction where Darth Vader travels back in time, his bond with Obi - Wan Kenobi would be full of possibilities. Imagine Vader going back to a time when he was still Anakin. He might have a newfound respect for Obi - Wan, knowing all that Obi - Wan tried to do for him in the future. Obi - Wan, for his part, could be shocked to see this changed Anakin. They could form an alliance against the emerging threat of the Sith, or Vader could try to get Obi - Wan to understand his view of the Force. Their relationship would no longer be simply that of a Jedi and his fallen apprentice, but something far more nuanced and unpredictable.
Count Dooku could be a prominent character. Given his own fall to the dark side, he might be a mentor or a rival to Obi - Wan in the fanfiction. Mace Windu is another one. His strict view of the Jedi Code and his relationship with Obi - Wan could be explored in the context of Obi - Wan's turn. And of course, there are the various Sith Lords and dark side adepts that might surround Obi - Wan, either as allies or enemies in his new dark side life.
Often, Obi - Wan uses his mastery of the Force. He might use a Force - push to overpower his guards when they least expect it and then make a run for it. He could also use a mind trick on a high - ranking captor to order his release.
Jon Snow could be one. He has a sense of honor and leadership, much like Obi - Wan. They could bond over their shared values and Jon could learn from Obi - Wan's wisdom. Another could be Daenerys Targaryen. She is on a quest for power and Obi - Wan might see her as someone who needs guidance to use her power responsibly.