  We report the discovery of three stars that, along with the prototype
LP40-365, form a distinct class of chemically peculiar runaway stars that are
the survivors of thermonuclear explosions. Spectroscopy of the four confirmed
LP 40-365 stars finds ONe-dominated atmospheres enriched with remarkably
similar amounts of nuclear ashes of partial O- and Si-burning. Kinematic
evidence is consistent with ejection from a binary supernova progenitor; at
least two stars have rest-frame velocities indicating they are unbound to the
Galaxy. With masses and radii ranging between 0.20-0.28 Msun and 0.16-0.60
Rsun, respectively, we speculate these inflated white dwarfs are the partly
burnt remnants of either peculiar Type Iax or electron-capture supernovae.
Adopting supernova rates from the literature, we estimate that ~20 LP40-365
stars brighter than 19 mag should be detectable within 2 kpc from the Sun at
the end of the Gaia mission. We suggest that as they cool, these stars will
evolve in their spectroscopic appearance, and eventually become peculiar O-rich
white dwarfs. Finally, we stress that the discovery of new LP40-365 stars will
be useful to further constrain their evolution, supplying key boundary
conditions to the modelling of explosion mechanisms, supernova rates, and
nucleosynthetic yields of peculiar thermonuclear explosions.

Solar and Stellar Astrophysics