  The compact binary radio pulsar system J0453+1559 (Martinez et al. 2015)
consists of a recycled pulsar as primary component of $1.559(5)\,M_\odot$ and
an unseen companion star of $1.174(4)\,M_\odot$. Because of the relatively
large orbital eccentricity of $e = 0.1125$, it was argued that the companion is
a neutron star, making it the neutron star with the lowest accurately
determined mass to date. However, a direct observational determination of the
nature of the companion is currently not feasible. Moreover, state-of-the-art
stellar evolution and supernova modeling are contradictive concerning the
possibility to produce such a low-mass neutron star remnant. Here we challenge
the neutron star interpretation by reasoning that the lower-mass component
could instead be a white dwarf born in a thermonuclear electron-capture
supernova (tECSN) event, in which oxygen-neon deflagration in the degenerate
stellar core of an ultra-stripped progenitor ejects several $0.1\,M_\odot$ of
matter and leaves a bound ONeFe white dwarf as the second-formed compact
remnant. We determine the ejecta mass and remnant kick needed in this scenario
to explain the properties of PSR~J0453+1559 by a neutron star--white dwarf
system. More work on tECSNe is needed to assess the viability of this scenario.
