A star dies when fusion in its core stops. Presumably this means that there is no longer any fusionable material in the core. Does this mean that there is no longer any fusionable material in the entire star or just that the stuff in the center is used up? For instance, suppose the star stats out as a ball of hydrogen. The hydrogen in the core is fused into helium - but the hydrogen away from the core is not. Is this exterior hydrogen cycled into the core and eventually depleted or does most of the hydrogen remain unfused at star death? What percentage of the hydrogen actually gets fused?