Alright... My current working theory is that Hikako is actually the one who died, and Sachiko has become entirely delusional in order to deal with the grief. She believes herself to be Hikako, and thinks that Sachiko has been dead or missing, when in reality she is misremembering her life by overlaying the memories of her girlfriend over her own life. This would explain why, regardless of Hikako's status as someone who has been observed to be in a psych ward, a funeral for somebody still took place, which Sachiko supposedly attended. This would also explain why the doctor has a room set up for Sachiko specifically. Sachiko (from the player's perspective) has a room in the hospital, and a life outside of the ward simultaneously, however Takako has only been seen inside the ward as of yet.
