The Final Days are a series of Quest introduced in The Final Shape that can be picked up from Micah-10 in The Lost City.
Overview
In each quest, Micah will send you to find an unpartnered Ghost somewhere in the system and bring them back to help heal the Traveler before the final assault on the Witness. You will need to find a calcified statue of an enemy, Guardian or surreal imagery associated with the Witness in an activity, such as a Story mission, Strike, Battleground, etc., and scan them with their Ghost to get telemetry for the Ghost's location. Afterwards, they will need to find the Lost Ghosts in patrol in an area highlighted on the map, which will be found near more calcified statues. Once the Ghost is collected, they will need to be brought back to the Pale Heart. Once completed, Micah will reward you with pieces of the First Ascent armor, Deepsight Pale Heart weapons, and materials like Strange Coins and Ascendant Shards.
Additionally, though not recommended, these quests can be completed after the completion of Excision.