It is well known that neutron stars are born during the death of massive stars in iron core-collapse supernovae. However, they can also form via more exotic formation scenarios like the accretion-induced collapse of a white dwarf star in a binary system. I will show some results of formation scenarios of neutron stars formed via the collapse of a heavy white dwarf, and comment on their potential detectability with gravitational radiation. While the implementation of a sophisticated method to deal with the common envelope phase in binary population synthesis is still a work in progress, preliminary results show that we may be able to constrain common envelope physics with accretion-induced collapse (and also Type Ia supernova) progenitors using future space-based gravitational wave detectors.