  What happens to a neutron star or white dwarf near its maximum mass limit
when it is brought into a close binary orbit with a companion? Such situation
may occur in the progenitors of Type Ia supernovae and in coalescing neutron
star binaries. Using an energy variational principle, we show that tidal field
reduces the central density of the compact object, making it more stable
against radial collapse. For a cold white dwarf, the tidal field increases the
maximum stable mass only slightly, but can actually lower the maximum central
density by as much as $30\%$. Thus a white dwarf in a close binary may be more
susceptible to general relativistic instability than the instability associated
with electron capture and pycronuclear reaction (depending on the white dwarf
composition). We analyse the radial stability of neutron star using
post-Newtonian approximation with an ideal degenerate neutron gas equation of
state. The tidal stablization effect implies that the neutron star in
coalescing neutron star-neutron star or neutron star-black hole binaries does
not collapse prior to merger or tidal disruption.
