  The evolution of many close binary and multiple star systems is defined by
phases of mass exchange and interaction. As these systems evolve into contact,
tidal dissipation is not always sufficient to bring them into circular,
synchronous orbits. In these cases, encounters of increasing strength occur
while the orbit remains eccentric. This paper focuses on the outcomes of close
tidal passages in eccentric orbits. Close eccentric passages excite dynamical
oscillations about the stars' equilibrium configurations. These tidal
oscillations arise from the transfer of orbital energy into oscillation mode
energy. When these oscillations reach sufficient amplitude, they break near the
stellar surface. The surface wave-breaking layer forms a shock-heated
atmosphere that surrounds the object. The continuing oscillations in the star's
interior launch shocks that dissipate into the this atmosphere, damping the
tidal oscillations. We show that the rapid, nonlinear dissipation associated
with the wave breaking of fundamental oscillation modes therefore comes with
coupled mass loss to the wave breaking atmosphere. The mass ratio is an
important characteristic that defines the relative importance of mass loss and
energy dissipation and therefore determines the fate of systems evolving under
the influence of nonlinear dissipation. The outcome can be rapid tidal
circularization ($q\ll1$) or runaway mass exchange ($q\gg1$).
