Structured liquids stabilized by interfacial assemblies enable spatial control over chemical systems. To prescribe a lifetime for structured liquids requires that the interfacially trapped material eventually reverts to molecularly dissolved species. Here, we show that poly(acrylic acid) fueled with carbodiimide segregates to an oil-water interface and forms assemblies of aggregates, solidifying the interface. When the fuel is consumed, the assembly dissipates into soluble polymer chains, destroying any out-of-equilibrium structure imparted to the liquid. We exploit this phenomenon to control liquid compartment temporal stability. Using interfacial rheology, we identify crossover points in the interfacial storage and loss moduli at times commensurate with the fuel concentration, evidencing transitions from solid-like to liquid-like assemblies that cause compartmentalized liquids to burst. These solid-like assemblies demonstrate reduced permeability to dye, showing the potential of this system for timed partitioning or release of chemical species. This work opens a pathway to time- and shape-programmable chemical systems.