Johnsy is very weak and does not have a strong stitution initially to fight off the weakness that her body had created after becoming ill. She essentially gives up; which does not seem to make her much of a fighter. She is well cared about and has good friends or the people around her, her roommate and the artist below, would not have tried so hard to help her.
Once she sees the leaf lasting Johnsy begins to change. She mentally becomes a stronger person as she tries to endure like the leaf had endured.