One common theme could be her struggle to regain her sense of self. After experiencing abuse, she might be shown trying to find her old strength and identity. Another could be her relationships being affected, like with Peeta or Gale. Maybe they try to help her through it or there are strains because of what she's been through.
There might be some out there. However, fanfiction can vary greatly in quality and content. Some might handle the topic in a more tasteful way, perhaps focusing on her emotional abuse and how she overcomes it within the context of the story's themes. But it's also important to approach such content with caution as it can be a sensitive area.
I'm not really into promoting or specifically naming fanfictions about abuse as it's a rather dark and disturbing topic. However, you can search on major fanfiction platforms like Archive of Our Own and filter the results for Katniss and Peeta stories. Look for tags that might indicate more complex or difficult themes, but be prepared for some heavy content.
In some fanfictions, Katniss might be depicted as pregnant. Fanfiction allows for a wide range of creative interpretations of the characters. However, in the original 'Hunger Games' series, there is no such plot. So it depends on the specific fanfiction you are reading.
Gale might also attempt to rescue Katniss. He's her friend from District 12 and is quite skilled in his own right. He would be furious to hear that Cato has kidnapped Katniss and would likely gather resources and allies to try and save her.
Her character could develop a new level of determination. Before, she was fighting for her family and district. Now, with a baby on the way, she has an even greater reason to survive. She might become more calculating, using her wits to avoid dangerous situations rather than charging in head - first. She would also probably show more vulnerability, as the pregnancy adds an extra layer of stress and worry.
Katniss would likely become more protective. Her natural instinct to survive would be amplified by the need to protect her unborn child. This could make her more cautious in her actions in the arena, but also more fierce when directly threatened.
She might get angry. Katniss has a fiery side, and seeing Peeta with another girl could trigger that. She could give Peeta the cold shoulder and refuse to talk to him.
In the original Hunger Games, Katniss and Peeta's relationship was mainly about survival, mutual protection, and the fight against the Capitol. In abused fanfictions, it takes a dark turn. Their characters are put in situations where they are victims of abuse, which is completely different from their roles in the original story where they were strong and defiant. For example, in the original, they were the symbols of hope for the districts, not helpless victims as in the abused fanfictions.
Katniss would likely be determined to get Peeta back to his normal self. So, instead of just retaliating, she would focus on finding a cure or a way to reverse the hijacking. She might isolate herself with Peeta in a safe place to try and break through to him, using her own memories and emotions to reach the real Peeta hidden inside the hijacked version.