  The continuing difficulty of achieving a reliable explosion in simulations of
core-collapse supernovae, especially for more massive stars, has led to
speculation concerning the observable transients that might be produced if such
a supernova fails. Even if a prompt outgoing shock fails to form in a
collapsing presupernova star, one must still consider the hydrodynamic response
of the star to the abrupt loss of mass via neutrinos as the core forms a
protoneutron star. Following a suggestion by Nadezhin (1980), we calculate the
hydrodynamical responses of typical supernova progenitor stars to the rapid
loss of approximately 0.2 to 0.5 M_sun of gravitational mass from their
centers. In a red supergiant star, a very weak supernova with total kinetic
energy ~ 10^47 erg results. The binding energy of a large fraction of the
hydrogen envelope before the explosion is of the same order and, depending upon
assumptions regarding the neutrino loss rates, most of it is ejected. Ejection
speeds are ~ 100 km/s and luminosities ~ 10^39 erg/s are maintained for about a
year. A significant part of the energy comes from the recombination of
hydrogen. The color of the explosion is extremely red and the events bear some
similarity to "luminous red novae," but have much lower speeds.
