Drawing on the experiences of the historical Eurodollar market and recent Chinese dollar bond issuances traded outside US jurisdiction at negative spreads to Treasuries, we examine the conditions under which a parallel offshore dollar financial system that circumvents Western sanctions may emerge. We propose a model in which liquidity provision and a safe bond supply drive currency use. We characterize three equilibrium regimes: High convenience yields emerge in both the initial sanctions-driven region and the final liquidity-driven region, separated by an intermediate region. Transitions between equilibria depend on safe-asset supply and liquidity technologies, in addition to endogenous dynamic complementarities.