Fugitive Demon King.

All the demons till the high-rank level need sin energy. A low concentration of sin energy will prevent them from growing. The absence of sin energy will cause them to start to die. The sin energy in their body will escape forcefully into the surroundings and they will weaken. They can prolong their lives by eating each other but they are doomed unless sin energy is made available again.

The detachment of the plane will also cause it to be disconnected from the demon sire so there won't be production of new demon fledglings. Demon nobles and the demon dukes will be alright in the absence of sin energy. 

But the plane needs the energy. It won't be able to run without a constant supply of energy. A prolonged lack of energy will cause it to start to break down. Any demon king that detaches his or her plane will need to reconnect it soon or risk losing the entire plane and becoming a plane-less demon king.