A prevalent trope can be her trying to limit her partner's exposure to certain characters she deems untrustworthy. In the RWBY world, which is full of various characters with different motives, she might not want her partner to interact with those who have a more ambiguous moral standing. This can create a lot of conflict and drama within the fanfiction.
One common trope is the overprotective girlfriend being overly cautious about her partner's battles. For example, she might try to keep him from taking on dangerous missions in the RWBY universe. Another is her getting jealous easily when others get too close to her partner during team interactions.
She could also be shown as having a strong sense of worry. Maybe she has nightmares about her partner getting seriously injured in a Grimm attack and then becomes even more overprotective in the real world. She might start to limit his activities outside of the safety of their base or team.
One common theme is loyalty. The overprotective sister is often extremely loyal to her sibling, willing to go to great lengths to keep them safe. For example, she might put herself in danger without hesitation.
Another common theme might be the contrast between Ruby's overprotective side and her normal, more carefree self. In the fanfiction, the author could play with this contrast, showing how Ruby is usually a positive and enthusiastic person, but when it comes to the safety of her team, she becomes a completely different, more intense person. This can add depth to her character and also create interesting storylines within the fanfiction.
A frequent trope is the overprotective big sister being extremely possessive. She sees the male reader as her 'little boy' even when he's grown. In some fanfictions, this can lead to conflicts within the family. Also, she may be the first to jump to his defense in any situation, whether it's a minor argument with a neighbor or a more serious issue at school or work. She's like his personal bodyguard in a sense.
One common trope is the 'fish out of water' scenario. RWBY characters in the unfamiliar and often cutthroat world of Westeros. Another is the power struggle trope. Since both universes have elements of power - seeking characters. A third trope could be the 'unlikely alliance'. For example, a RWBY character teaming up with an underdog in Game of Thrones against a common enemy.
One common trope is the 'coming out' story. The trans character in RWBY fanfiction has to find the right moment to reveal their true identity to their friends or teammates. Another is the 'finding acceptance' trope, where they face initial doubts or even hostility but eventually find a place where they are fully accepted.
There's also 'Overprotective Ruby' which focuses on Ruby being overly protective of her sister or friends. It has some really interesting scenarios where Ruby's protectiveness gets her into both comical and tense situations. This fanfiction does a great job of exploring Ruby's character in this context.
One common trope is the 'Fish out of Water' where the main character, often a self - insert or an original character, finds themselves in the RWBY universe and attracts the attention of multiple characters from the show, forming a harem. For example, a character from our world suddenly ends up at Beacon Academy and has to adapt while dealing with the romantic interests of Ruby, Weiss, Blake, and Yang.
One common theme is Batman being overly protective of his sidekicks like Robin. He might go to extreme lengths to keep them out of danger, even if it means restricting their actions. For example, he could forbid Robin from going on certain missions that he deems too risky.
A lot of these fanfics also use the 'unexpected kidnapper' trope. It could be someone who was thought to be an ally or a new, unknown enemy. This adds an element of surprise to the story. And there's often the trope of Ruby's friends having to overcome their own personal issues or insecurities in order to rescue her successfully.