Phoenix is referring to the idea that the rest of her family is dead. She and her grandson are the only two remaining members of her family. This fact gives Phoenix the motivation to take such an arduous journey and to be so persistent in getting him help. If her were to die, she would be left alone, as the last one in her family. She wants to see her family survive and that means the grandson must grow up and have children of his own. The name "Phoenix" also implies this. The Phoenix was a mythical bird which would burn itself up only to rise from the ashes. Phoenix's family is almost gone and the only hope it has of "rising from the ashes" is her grandson.