[Butterknife]

Going by Misa-chan's interpretation. Maybe Ayumi wants to be granted time to be in the human world, so she can see the man she loved for the last time. Maybe that man she used to love is the old man, and after time passed she wanted to come back to earth to see him again. Also in the video, the man is looking at a locket at one point, maybe he's reminiscing his and her time together. Then at the end when Ayumi is about to be reunited one last time with the man she loved a long time ago, she dissapears.. It's really sad..