  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 letter 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 be disrupted by tidal interactions. This
can have profound implications on the final outcomes of triple star-systems.
