Statement I is correct because \( S_8 \) can indeed undergo disproportionation in alkaline medium:
\[ S_8 + 12 \text{OH}^- \rightarrow 4 S^{2-} + 2 S_2O_3^{2-} + 6 H_2O. \]
Statement II is incorrect because \( \text{ClO}_4^- \) cannot undergo disproportionation as chlorine is already in its highest oxidation state.
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