Tsuki wa Higashi ni Hi wa Nishi ni: Operation Sanctuary

Naoki Kuzumi lives with his aunt, uncle, and cousin Matsuri after his parents' death in an accident five years ago. He has no memory of his youth, but his life is ordinary otherwise. Mikoto, a redheaded girl, literally falls onto him from the sky while he's napping, believing him to be her younger brother. This coincides with Naoki existing in a temporal shelter from the future, where many are suffering from an incurable disease; Mikoto had traveled back in time to find her brother Yuusuke, who was supposedly taken to Naoki's time.