  The Magellanic Stream is sculpted by its infall through the Milky Way's
circumgalactic medium, but the rates and directions of mass, momentum, and
energy exchange through the Stream-halo interface are relative unknowns
critical for determining the origin and fate of the Stream. Complementary to
large-scale simulations of LMC-SMC interactions, we apply new insights derived
from idealized, high-resolution "cloud-crushing" and radiative turbulent mixing
layer simulations to the Leading Arm and Trailing Stream. Contrary to classical
expectations of fast cloud breakup, we predict that the Leading Arm and much of
the Trailing Stream should be surviving infall and even gaining mass due to
strong radiative cooling. Provided a sufficiently supersonic tidal swing-out
from the Clouds, the present-day Leading Arm could be a series of high-density
clumps in the cooling tail behind the progenitor cloud. We back up our analytic
framework with a suite of converged wind-tunnel simulations, finding that
previous results on cloud survival and mass growth can be extended to high Mach
number ($\mathcal{M}$) flows with a modified drag time $t_{drag} \propto 1 +
\mathcal{M}$ and longer growth time. We also simulate the Trailing Stream; we
find that the growth time is long ($\sim$ Gyrs) compared to the infall time,
and approximate H$\alpha$ emission is low on average ($\sim$few mR) but can be
up to tens of mR in bright spots. Our findings also have broader extragalactic
implications for e.g. galactic winds, which we discuss.
