The government could indeed exist alone without state, but the sovereign can survive without the administration.
To be called a state, it must consist of four components. Such as land for people to live on, a governance to make the law and regulations for them to obey, and a commodity for the residents to enjoy under external supervision, although a government may exist without a state.
Sovereign nations are defined by international treaties as having a permanent people, a defined territory, a single government, and the ability to interact with other sovereign states.
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