The disappearance of the ISD Exodus had managed to capture the imagination, or rather the greed, of several major factions within the Galaxy. The Galactic Empire, the New Republic, both would dispatch significant assets into the Unknown Regions for the purpose of hunting down and recovering the Exodus for their respective faction and, more importantly, also acquire it's valuable cargo along with it. Due to the importance placed upon the Exodus, tales of what it contained would spread far and wide with some saying it was filled to the brim with credits and other valuables whilst others claimed it contained top secret schematics and blueprints that would give whoever held it an invaluable edge in the Galactic Civil War. Regardless of what it actually contained, the hunt for it would be something of an adventure in and of itself with both the Empire and the New Republic scouring the Unknown Regions for the missing Star Destroyer and undergoing various trials and tribulations in the process as the extended time away from civilisation took it's toll upon those intrepid explorers tasked with the Exodus' recovery.
Of the two factions racing towards the Exodus, it would be the New Republic that would discover it first. After intercepting a garbled distress transmission originating in the Tempered Wastes, a region of space not known for having much of anything, the assets dispatched by the New Republic, which included Rogue Squadron, led by Wedge Antilles, and Maalraas Squadron, led by Ghes Ordo, would converge on the region as they narrowed their search. With the number of planets the Exodus might have fled to narrowed down, the New Republic would eventually discover the ISD Exodus in the Lehon System where Rogue Squadron would find the Exodus crashed upon the surface of the uninhabited planet. The answer to why the Exodus had crashed on the planet would forever remain a mystery to the New Republic, interrogation of the crew yielded few answers, however that it was intact enough for recovery was sufficient for the New Republic to commit to recovering whatever they could from the wreck on the planet's surface.
After detaining the crew and a number of refugees who appeared to have been seeded in with them for whatever reason, in order to prevent interference in the recovery process, the crew and refugees would be kept some distance away from the Exodus and under constant guard with any misbehaviour being answered with gunfire, the New Republic began the process of stripping the Exodus of anything of value. Databanks containing the locations of several other such "Vault Ships" would be discovered along with a second cache equal in size to the one at Wayland as well as a number of artifacts and relics dating as far back as the Jedi Civil War. Several incidents would occur during the recovery process, most involving Ghes Ordo who got into a brawl with an unnamed crew member and then opened fire in the Exodus after claiming to have seen someone stalking the halls, a claim that was dismissed, but on the whole, the affair would go smoothly. Upon the arrival of Imperial assets in the Lehon System, including the famed 181st Squadron, the New Republic would withdraw their forces and depart for the Luke System after blowing the Exodus from orbit and leave the wreckage to the Empire.
The Empire would itself gain a far more complete picture of just what happened to the ISD Exodus after confirming that the New Republic had departed the system. Whilst the Imperial Navy tended to the survivors, several would be killed and many more wounded when the New Republic destroyed the Exodus from orbit with dust and debris being kicked up by the bombardment, high-ranking officers would be debriefed by Captain Hux and other Imperial officers. It would be discovered that following the Battle of Endor, the ISD Exodus had jumped to the Bakura System seeking resupply just in time to be caught up in the Ssi-ruuk Invasion, an invasion which the ISD Exodus had little ability to stop and therefore made swift preparations to depart from the system. Due to a number of people seeking refuge on the ship, and with overriding orders being given from the previously mentioned Countess whose authority is believed to outstrip even the Director's, the Exodus would delay long enough to take on a significant number of refugees before making an uncalculated jump away from Bakura. Due to the damage sustained during the attack and the subsequent jump, the Exodus crashed shortly after dropping out of hyperspace, ultimately crashing into Lehon where it remained until the arrival of the New Republic.
This story would itself be confirmed in private by the Countess, who confirmed her status as the Emperor's Hand after being confronted with the appropriate codes, who would nevertheless withhold further information until she was debriefed by the new Empress. With the Exodus lost to the Empire and it's crew recovered, the Empire would then withdraw from the system, dropping the refugees off at Nirauan for Thrawn to carry the rest of the way home, and report back to Coruscant with work of the Exodus' loss.
Summary
New Republic discovers the Exodus first.
Artifacts, relics, and information on other caches recovered.
Imperial arrival prompts the New Republic to destroy the Exodus and flee the system.
Imperials recover the crew and refugees as well as the "Countess Claria".