We present results of simulations of stellar collapse and explosions in spherical symmetry for progenitor stars in the 8–$10\,M_\odot$ range with an O-Ne-Mg core. The simulations were continued until nearly one second after core bounce and were performed with the Prometheus/Vertex code with a variable Eddington factor solver for the neutrino transport, including a state-of-the-art treatment of neutrino-matter interactions. Particular effort was made to implement nuclear burning and electron capture rates with sufficient accuracy to ensure a smooth continuation, without transients, from the progenitor evolution to core collapse. Using two different nuclear equations of state (EoSs), a soft version of the Lattimer & Swesty EoS and the significantly stiffer Wolff & Hillebrandt EoS, we found no prompt explosions, but instead delayed explosions, powered by neutrino heating and the neutrino-driven baryonic wind which sets in about 200 ms after bounce. The models eject little nickel (${<} 0.015~M_\odot$), explode with an energy of ${\ga}0.1\times 10^{51}\,$erg, and leave behind neutron stars (NSs) with a baryonic mass near $1.36\,M_\odot$. Different from previous models of such explosions, the ejecta during the first second have a proton-to-baryon ratio of $Y_{\rm{e}} \ga 0.46$, which suggests a chemical composition that is not in conflict with galactic abundances. No low-entropy matter with $Y_{\rm{e}} \ll 0.5$ is ejected. This excludes such explosions as sites of a low-entropy r-process. The low explosion energy and nucleosynthetic implications are compatible with the observed properties of the Crab supernova, and the small nickel mass supports the possibility that our models explain some subluminous type II-P supernovae.