The Rift (狭間 Hajima) is a plane of existence that works as a bridge between the living and dead in Fatal Frame III: The Tormented. Located deep under the Kuze Shrine, it appears as a long beach with a body of water reaching far out, which leads to the Abyss of the Horizon, the final resting place for souls.
There also exists a part of the rift held within dreams. The origin of the ritual existed as a way for people to come to the shrine and give their pain of loss and sorrow through the Tattooed Priestess, who would receive a tattoo made from special ink, containing a physical form of their suffering.
The Rift requires a sacrifice to remain at bay, so the sleeping tattooed priestess would be cast out of a boat to the other side, bearing the tattoos of suffering as an offering.
However, the last tattooed priests, Reika Kuze, had the tattoo enter her eyes, which reflected the pain she held back to the living, and caused the unleashing and miasma to spread across the manor. While corrupting and extremely power, the miasma did not kill immediately, allowing Yashuu Kuze to try to prevent the spread by having the carpenters sacrifice themselves as human pillars and the handmaidens to impale themselves. Eventually, the manor became a massive fortress able to contain the spread and kept those trapped within a dream state.
Due to Reika’s desire to spread her pain, people greatly affected by lose are susceptible to being pulled into the Manor of Sleep through their dreams. They too become cursed after being touched by Reika within the manor. Rei Kurosawa was able to put a stop to Reika, allowing her to finally sleep forever along with her lover, Kaname. Sending them both across the Rift and finally ending the tattoo curse and allowing the trapped souls to cross over, finding peace.