Inosuke survives throughout the manga. The story doesn't have his death as part of the plot. His character remains active and plays a significant role until the end.
First, you need to understand Inosuke's character really well. Know his strengths like his amazing physical abilities and his weaknesses like his lack of social graces. Then, choose the world you want to cross him over with. For example, if it's a fantasy world, figure out how his abilities would work there.
Well, Inosuke's origin story is quite interesting. He was found in the mountains as a baby and was raised by a family of boars. This led to his rather unorthodox and savage behavior. He didn't have any proper human upbringing which is why he often acts on his instincts. For example, he is very aggressive in battles and doesn't really follow the normal social norms that other characters do. His origin also influenced his unique fighting style which is very much based on brute force and his animal - like agility.
Inosuke doesn't become a Hashira in the manga. The story progresses with him having other significant experiences and achievements instead of achieving that specific position.
Inosuke doesn't die. The author keeps him alive to continue his adventures and growth. His character's resilience and fighting skills enable him to avoid death.
There's also a crossover with the My Hero Academia world. In this fanfic, Inosuke has to deal with quirks and the whole hero society concept. His lack of understanding of the 'normal' ways in society makes for some hilarious and action - packed scenes as he just barrels through situations.