From Pluralpedia, the collaborative plurality dictionary
core-kin (n., adj.)
Applies toheadmates, system functions

Core-Kin refers to a headmate who will take the place of the core. They become a headmate who has enough knowledge and awareness to take the mantle of the core. The core’s memories and attributes do not fuse with said headmate. Instead, the core’s memories and attributes are used as resources for said headmate to function independently, masking, acting as, or playing the part of the core, until said headmate is ready to function on their own.

This does not change anything; the status and role of anyone and anything in the system is not changed directly.

Core-Kin is only done with the core. None of the other system members are directly affected by this. The others may not interact with said headmate the same as they had interacted with the core, and develop individual relations different than ones had with the core.