In a 'kokushibo meets tanjiro fanfiction', one possibility is that Kokushibo senses something different about Tanjiro right away. Maybe it's the fact that Tanjiro has a unique scent or an energy that Kokushibo has never encountered before. Tanjiro, being Tanjiro, would be ready to face Kokushibo head - on, but also be open to communication if there's a chance. The story could explore their different views on the world of demons and slayers, and how they might come to understand each other better through their encounter.
For Tanjiro, he could become more understanding of the complex nature of demons. Meeting Kokushibo, a powerful and complex demon, might make him realize that not all demons are simply evil. Kokushibo, on the other hand, could start to have some doubts about his loyalty to Muzan. Tanjiro's tenacity and belief in the good of all might start to chip away at Kokushibo's cold - hearted exterior.
One common theme is the exploration of their relationship. Given their different personalities in the original work, fanfictions often focus on how they bridge the gap between them, like how Giyuu's stoicism and Shinobu's more cheerful yet calculating nature interact.
The battle of Yoriichi vs Kokushibo can be found in the advanced stages of the Demon Slayer manga. It's an intense and highly anticipated confrontation. The build-up and action are both masterfully depicted.
One common theme is the exploration of their contrasting personalities. Shinobu is often seen as more outgoing and mischievous while Giyuu is more stoic. Fanfics like to play with how these two different personalities interact and find common ground. Another theme is the idea of healing. Given their experiences in the main story, fanfics may show how they heal each other's emotional wounds.