The Faded Crisis Fragment is essential for unlocking the Arbiter of Ash because it is one of the three unique and rare Crisis Fragments required to access the Burning Monolith, the arena where the Arbiter of Ash fight takes place. Specifically, you need to collect three different Crisis Fragments: the Ancient Crisis Fragment, the Weathered Crisis Fragment, and the Faded Crisis Fragment.
You obtain the Faded Crisis Fragment by defeating the boss in the Copper Citadel, a special high-tier dungeon found in Tier 15+ maps on the Atlas. Each Crisis Fragment corresponds to a different Citadel and its specific boss. Collecting all three fragments is necessary to unlock the sealed door in the Burning Monolith. This door acts as a lock that requires all three Crisis Fragments to open, allowing you to initiate the fight against the Arbiter of Ash.
Without the Faded Crisis Fragment, you cannot start the Arbiter encounter, making it a mandatory item in your progression toward this pinnacle endgame boss. After placing all three fragments, the door opens, and you can descend into the Arbiter’s lair for this challenging encounter.
The Faded Crisis Fragment is critical because it serves as a key item necessary alongside the other two fragments to unlock the door in the Burning Monolith and engage the Arbiter of Ash boss fight, marking a major milestone in Path of Exile 2's endgame progression.