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Abstract Triple stellar systems allow us to study stellar processes that cannot be attained in binary stars. The evolutionary phases in which the stellar members undergo mass exchanges can alter the hierarchical layout of these systems. Yet, the lack of a self-consistent treatment of common-envelope (CE) in triple-star systems hinders the comprehensive understanding of their long-term fate. This paper examines the conditions predicted around binaries embedded within CEs using local 3D hydrodynamical simulations. We explore varying the initial binary separation, the flow Mach number, and the background stellar density gradients as informed by a wide array of CE conditions, including those invoked to explain the formation of the triple system hosting PSR J0337+1715. We find that the stellar density gradient governs the gaseous drag force, which determines the final configuration of the embedded binary. We observe a comparable net drag force on the center of mass but an overall reduction in the accretion rate of the binary compared to the single-object case. We find that, for most CE conditions, and in contrast to the uniform background density case, the binary orbital separation increases with time, softening the binary and preventing it from subsequently merging. We conclude that binaries spiraling within CEs become more vulnerable to disruption by tidal interactions. This can have profound implications on the final outcomes of triple-star systems.