Yggjrasil

She's Fuka, the heroine of the 4th game. Details are sparse, but she was scheduled to go to Hell and turn into a Prinny to pay for her sins, but the management of Hell/Heaven got so corrupt, there were simply too many prinnies being made, they ran out of prinny skins/bodies to give people. So they decided to just give her a hat and call it a day.