Well, I'm going to imagine this could be like the Pokemon Mystery Dungeon series. I myself was once a human, but I turned into my fursona. I would probably have no recollection of what happened before then, only with a fuzzy memory of what happened the night before. I would try to survive the world as life throws scenarios at me, and I would try to make friends and a new family to try and find out what happened, and why we were all there. Almost like Maze Runner. We would try to find a way to regain our memories of our past, and escape this world.
Personally, I would love to be my fursona, but I'd rather accomplish that with a fursuit, not survival in a video game. But all in all, I agree with Amy G, this would be fun to write about.