  The terrestrial detection of a neutrino burst from the next galactic
core-collapse supernova (CCSN) will provide profound insight into stellar
astrophysics, as well as fundamental neutrino physics. Using Time-Of-Flight
(ToF) effects, a CCSN signal can be used to constrain the absolute neutrino
mass. In this work, we study the case where a black hole forms during
core-collapse, abruptly truncating the neutrino signal. This sharp cutoff is a
feature that can be leveraged in a ToF study, enabling strict limits to be set
on the neutrino mass which are largely model-independent. If supernova
neutrinos are detected on Earth in liquid scintillator detectors, the
exceptional energy resolution would allow an energy-dependent sampling of the
ToF effects at low neutrino energies. One promising experimental program is the
Jiangmen Underground Neutrino Observatory (JUNO), a next-generation liquid
scintillator detector currently under construction in China. Using
three-dimensional black hole-forming core-collapse supernova simulations, the
sensitivity of a JUNO-like detector to the absolute neutrino mass is
conservatively estimated to be $m_\nu < 0.39^{+0.06}_{-0.01}$ eV for a 95% CL
bound. A future-generation liquid scintillator observatory like THEIA-100 could
even achieve sub-0.2 eV sensitivity.
