The detection of the unusually heavy binary neutron star merger GW190425 marked a stark contrast to the mass distribution from known Galactic millisecond pulsars in neutron star binaries and gravitational-wave source GW170817. We suggest here a formation channel for heavy binary neutron stars in which massive helium stars, assembled after common envelope, remain compact and avoid mass transfer onto the neutron star companion and thus evade pulsar recycling. In particular we present three-dimensional simulations of the supernova explosion of the massive stripped helium star and follow the mass fallback evolution and the subsequent accretion onto the neutron star companion. We find that fallback leads to significant mass growth in the newly formed neutron star and that the companion does not accrete sufficient mass to become a millisecond pulsar. This can explain the formation of heavy binary neutron star systems such as GW190425, as well as predict the assembly of neutron star - light black hole systems. Moreover, this hints to the existence of a sizable population of radio-quiet double compact objects in our Galaxy. Finally, this formation avenue is consistent with the observed mass-eccentricity correlation of binary neutron stars in the Milky Way.
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