  First, I demonstrate the possible formation channel for neutron stars (NSs)
via the accretion-induced collapse (AIC) of oxygen-neon-magnesium (ONeMg)
composition white dwarfs (WDs) inside planetary nebulae (PNe; also so-called
symbiotic nebulae). A heavy mass loss via the stellar wind or during the the
roche-lobe overfilling (RLOF) mass-transfer may happen at the late evolutionary
phase of ONeMg WD - red giant (or asymptotic giant branch) star binaries, and
it might form nebulae with central accreting WD binaries. The nebulae might be
ionized the hot cores of giant stars or accreting WDs. Therefore, the accreting
WD inside the symbiotic nebulae might grow in mass to the Chandrasekhar limit
mass and collapse. Peculiar NSs born via the AIC of WDs inside the symbiotic
nebulae (PNe) may finally have WD companions and become the NS-WD systems, and
the Milky Way may contain tens of such kind of systems. Second, I introduce
another possibility for the formation of PNe (or pulsar wind nebulae) with
newborn NS via the core-merger-induced collapse during the common envelope
evolution of ONeMg WD binaries.
