In exchange for the materials the Daiyu needed to accomplish their plan, Jade forced them to exchange the yin soul kernel. Since Elder Daiyu and Loki believed the entity to be male, they didn't see any issue in the exchange. In reality, the entity didn't care about the yin or yang kernels. They were always meant to act as catalysts and nothing more. What it wanted the most was the potential of the universe itself, not the amalgamation of mortal talent.
This was what awoke Jade from her previous state of madness. The damage done to her soul by her Eostre Clan's Moon manifestation was reversed in an instant and she grasped onto her sanity once more.
It was after this happened that she enlisted Primrose's help to enter the Eostre Tombs to punish herself. After that, she remained there for over 30 years, while actually experiencing the equivalent of several hundred, maybe even thousand, due to the ice will.