We study the relationship between fair division with $\textit{subsidies}$ and $\textit{best-of-both-worlds}$ (BoBW) fairness for indivisible items. We prove a general reduction of BoBW existence to envy-freeability. Specifically, for any scale-free ex-post property $P$ (e.g., EF1, EFX, PO) and any scale-free valuation class $\mathcal{V}$ (e.g, additive, submodular, subadditive, monotone), if every instance in $\mathcal{V}$ admits a $P$-allocation that can be made envy-free using subsidies, then every such instance admits an ex-ante envy-free lottery supported on $P$-allocations. The proof uses linear programming duality. As applications, the reduction gives alternative proofs of BoBW existence results for additive goods, chores, and mixtures of goods and chores. The converse of our general reduction holds for two agents but fails for three: We provide a four-good counterexample with monotone submodular valuations where an ex-ante envy-free and ex-post EF1 lottery exists, but no allocation is simultaneously EF1 and envy-freeable. For lexicographic valuations, we prove simultaneous EFX, Pareto optimality, and envy-freeability (and hence BoBW guarantees for EFX+PO) for three agents, and show that even EFX and envy-freeability can be incompatible for four agents.

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