If the Womb of Grief has been completed, Alex will confront the protagonist following the defeat of Mem Aleph. Alex explains her backstory, which changes depending on the protagonist's alignment. From there, Alex entrusts the future and disappears as the one she comes from doesn't exist. However, following her disappearance, Demeter asks to see the Cosmic Fruit the two had collected. Regardless of the protagonist's decision, Demeter will take the fruits, and opens the way to the Empyrean Ascent.
If the protagonist goes back on his allegiance with Alex and chooses to fight her instead, she will become enraged and empowered, and fights alongside Amon, Shaytan, and a Tsuchigumo.
End of spoilers.
Trivia
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Nomenclature
Like the other sectors in the Schwarzwelt, Sector Horologium is named after a constellation, being Horologium.