Each time Zagreus (the protagonist) dies and "respawns" in the House of Hades, the characters within—like Achilles, Nyx, and Hades himself—have new dialogue reflecting your recent successes or failures.
The term appears in historical aeronautical engineering documents regarding "Hades Hub" specifications for propeller design. Hades Hub
While the video game is the most common association, the term also appears in specialized technical and security contexts: Description Each time Zagreus (the protagonist) dies and "respawns"