You have it completely backwards. No public institution has a right to exist.
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All public institutions exist to serve the public.
When they become ineffective at serving such a purpose, when the public need for such service lapses, when better or more efficient alternatives exist for serving such purposes, or when the public decides that said public service is less important than some other competing value, the state owes an obligation to the public to close the institution or reform the institution to meet the current and future needs.