Each mayor of Ember got told to keep the secret of the box in the basement of the Gathering Hall. Know one knew what was in there though. The seventh mayor was not as honorable as the rest. He got very sick so he took the box and hammered it to see if there was something in there that could heal him, Unfortunately for him, he died before he could see what was in there.
Lina became greedy when she saw that Looper was selling colored pencils and she wanted one even though she was supposed to buy a sweater for her grandmother. She decided to just buy one pencil and she would still have enough money to buy a sweater but instead she bought two colored pencils and no sweater. Her greed over took her, causing her to do the wrong thing.
Doon showed greed when he said and thought that he wanted to find the new city and be recognized for this. He only wanted Lina to accompany him because he did not want anyone else to get the glory. Over all, almost everyone showed a little bit of greed, even the main characters.