  A number of low-mass millisecond pulsar (MSP) binaries in their
rotation-powered state exhibit double-peaked X-ray orbital modulation centered
at inferior pulsar conjunction. This state, which has been known to persist for
years, has recently been interpreted as emission from a shock that enshrouds
the pulsar. However, the pressure balance for such a configuration is a crucial
unresolved issue. We consider two scenarios for pressure balance: a companion
magnetosphere and stellar mass loss with gas dominance. It is found that the
magnetospheric scenario requires several kilogauss poloidal fields for isobaric
surfaces to enshroud the MSP as well as for the magnetosphere to remain stable
if there is significant mass loss. For the gas-dominated scenario, it is
necessary that the companion wind loses angular momentum prolifically as an
advection or heating-dominated flow. Thermal bremsstrahlung cooling in the flow
may be observable as a UV to soft X-ray component independent of orbital phase
if the mass rate is high. We formulate the general requirements for shock
stability against gravitational influences in the pulsar rotation-powered state
for the gas-dominated scenario. We explore stabilizing mechanisms, principally
irradiation feedback, which anticipates correlated shock emission and companion
variability and predicts $ F_\gamma/F_{\rm X} \lesssim 14$ for the ratio of
pulsar magnetospheric $\gamma$-ray to total shock soft-to-hard X-ray fluxes.
This stability criterion implies an unbroken extension of X-ray power-law
emission to hundreds of keV for some systems. We explore observational
discriminants between the gas-dominated and magnetospheric scenarios,
motivating contemporaneous radio through $\gamma$-ray monitoring of these
systems.
