  Some massive stars end their lives as \textit{failed} core-collapse
supernovae (CCSNe) and become black holes (BHs). Although in this class of
phenomena the stalled supernova shock is not revived, the outer stellar
envelope can still be partially ejected. This occurs because the hydrodynamic
equilibrium of the star is disrupted by the gravitational mass loss of the
protoneutron star (PNS) due to neutrino emission. We develop a simple model
that emulates PNS evolution and its neutrino emission and use it to simulate
failed CCSNe in spherical symmetry for a wide range of progenitor stars. Our
model allows us to study mass ejection of failed CCSNe where the PNS collapses
into a BH within $\sim100\,{\rm ms}$ and up to $\sim10^6\,{\rm s}$. We perform
failed CCSNe simulations for 262 different pre-SN progenitors and determine how
the energy and mass of the ejecta depend on progenitor properties and the
equation of state (EOS) of dense matter. In the case of a future failed CCSN
observation, the trends obtained in our simulations can be used to place
constraints on the pre-SN progenitor characteristics, the EOS, and on PNS
properties at BH formation time.
