In the story Day would always go back to his old house to check up on his family. He would bring them medicine to help his little brother, Eden. It influend the plot becuase it one one of the reasons Day got caught. It was also where they found his siblings and killed his mom.
After Day jumps off of the building and hurts himself(after robbing the hospital) he passes out. He wakes up in the house of a stranger with his scavenger buddy,Tess. Tess was tending to his needs. This house is where he recoverd after his injury.
This is where Day spied on his family to make sure they were okay. He hid in there when the soldiers weren't patrolling their neighborhood. This helps develop the plot because when, he reveals himself, he hides his family there. Unfortunately, they were still found and punished unjustly.