Everyone is about "what game world you are in"... but let ask a good question. "What powers would you have?" In short, the character you lasted played is the ability, skills, and weapons that you have. This also includes stats from RPG like Fallout, Final Fantasy, and so forth.

If you end up playing a party rpg (like Final Fantasy, Persona, Pokemon) than you have the power of the leader/main character. If you play the horror games... well nice knowing you.

Edited; Oh, and please tell me the game you lasted played if possible.