Story

Second Eruption
The Core of Death first formed when the Will of the Honkai gave it to Sirin during the Second Eruption, it was and dubbed the Gem of Serenity. Through Sirin the Core's Soul was supressed and the Authority was utilised many times, while Sirin had it she was immortal. After a long fight with the MANTIS Siegfried Kaslana he removed the Core and killed her. After Siegfried was forced to leave the Core was later found in the ruins by Schicksal.
Schicksal Experiments
While the Core was in the hands of Schicksal it was used many times on innocent Valkyries in an attempt to turn them into Herrschers that could be controlled. Many Valkyries were trialled for it but in the end all died to exposure to the Core. The Valkyrie Lin Magi was the last test subject and looked to be accepting the Core well and could have birthed the Herrscher of Death but due to her not being strong enough she succumbed and was disintegrated by the power.
Singapore
The rouge Schicksal scientist Dr Magi managed to steal the Core from Schicksal after having had enough of all the loss of life. Dr Magi agreed to hand the Core over to Anti-Entropy to keep it out of the hands of Schicksal, and so was taken to the neutral area of Singapore. After Cocolia got her hands on it in Singapore she planned to use it to create the Herrscher of Death through creating a Honkai Eruption by shooting Honkai Energy into it until it became self sustaining. After Kiana and Dr Magi got to the Core Kiana was able to stop the Honkai Energy it was producing by holding it in her hands, however doing so allowed the Herrscher of the Void to awaken and wield the powers of the Herrscher of Death through the Core. After a battle with Fu Hua the Core was separated from Kiana and put into a storage contained that would stop the Honkai Energy flow.
Herrscher of the Void
Once the Herrscher of the Void began to reawaken in Kiana, Otto gave the Core of Death to her to speed up the process and grant her the Authority of the Herrscher of Death. While the Core was held by the Herrscher of the Void the Authority of Death would be used many times and the Soul of the Herrscher of Death continued to once again be supressed and was never given a chance to awaken into a Herrscher.
Herrscher of Flamescion
Once Kiana became the True Herrscher of the Void she channelled the Authorities of Death and Fire from their Cores actively and became known as the Herrscher of Flamescion. Due to the continued use of the Core of Death by another Herrscher, the Soul within continued to be further supressed.
Herrscher of Finality
Once Kiana made the choice to become an artificial Herrscher of Finality she drew the Authorities from all the Cores with help of the Herrscher of Origin, through this she was able to get close enough to the Herrscher of Finality that the Cocoon of Finality granted her access to the Authority of Finality. Due to being artificial Kiana continued to require use of all other Authorities to wield the Authority of Finality, so the Herrscher of Death Soul continued to be supressed within the Core.