We investigate the final collapse of rotating and non-rotating pulsational pair-instability supernova progenitors with zero-age-main-sequence masses of 60, 80, and 115 M and iron cores between 2.37 M and 2.72 M by 2D hydrodynamics simulations. Using the general relativistic NADA-FLD code with energy-dependent three-flavor neutrino transport by fluxlimited diffusion allows us to follow the evolution beyond the moment when the transiently forming neutron star (NS) collapses to a black hole (BH), which happens within 350-580 ms after bounce in all cases. Because of high neutrino luminosities and mean energies, neutrino heating leads to shock revival within 250 ms post bounce in all cases except the rapidly rotating 60 M model. In the latter case, centrifugal effects support a 10% higher NS mass but reduce the radiated neutrino luminosities and mean energies by ∼20% and ∼10%, respectively, and the neutrino-heating rate by roughly a factor of two compared to the non-rotating counterpart. After BH formation, the neutrino luminosities drop steeply but continue on a 1-2 orders of magnitude lower level for several 100 ms because of aspherical accretion of neutrino and shock-heated matter, before the ultimately spherical collapse of the outer progenitor shells suppresses the neutrino emission to negligible values. In all shock-reviving models BH accretion swallows the entire neutrino-heated matter and the explosion energies decrease from maxima around 1.5 × 10 51 erg to zero within a few seconds latest. Nevertheless, the shock or a sonic pulse moves outward and may trigger mass loss, which we estimate by long-time simulations with the P code. We also provide gravitational-wave signals.