Reading on the TYPE-MOON Wiki it says that Hibiki Hibino
...is the Holy Scripture Triten (聖典トライテン, ?) of Caubac Alcatraz
on Caubac Alcatraz's page it says in the second paragraph in his Abilities
He created a labyrinth inside a treasure chest that cannot be opened to protect his ideal terminal, the Holy Scripture Triten, but the reason he hasn't appeared for a century is because he accidentally became trapped inside.
Now obviously Arcueid can get to him as she states that it's "too troublesome to get to him while he is in his own world" probably referring to how the chest cannot be opened and probably the chest being near indestructible otherwise it's easy picking for the Church, but she seems to imply she can get inside anyway as she threatens to kill him in his own world when he enrages her by telling her that he was talking about her having found love like that of a human.
But the point of the labyrinth is to protect Holy Scripture Triten and it was Hibiki Hibino who handed the phone to Arcueid. So why isn't Holy Scripture Triten inside Caubac's Labyrinth? is Caubac even aware that she isn't in the Labyrinth?
I use tsukihime because of Arcueid and that Caubac Alcatraz is one of The Twenty-seven Dead Apostle Ancestors and these are more references in Tsukihime than Fate