  We study the evolution and final outcome of long-lived (${\approx}10^5$
years) remnants from the merger of a He white dwarf (WD) with a more massive
C/O or O/Ne WD. Using Modules for Experiments in Stellar Astrophysics
($\texttt{MESA}$), we show that these remnants have a red giant configuration
supported by steady helium burning, adding mass to the WD core until it reaches
$M_{\rm core}\approx 1.12-1.20 M_\odot$. At that point, the base of the surface
convection zone extends into the burning layer, mixing the helium burning
products (primarily carbon and magnesium) throughout the convective envelope.
Further evolution depletes the convective envelope of helium, and dramatically
slows the mass increase of the underlying WD core. The WD core mass growth
re-initiates after helium depletion, as then an uncoupled carbon burning shell
is ignited and proceeds to burn the fuel from the remaining metal-rich extended
envelope. For large enough initial total merger masses, O/Ne WD cores would
experience electron-capture triggered collapse to neutron stars (NSs) after
growing to near Chandrasekhar mass ($M_{\rm Ch}$). Massive C/O WD cores could
suffer the same fate after a carbon-burning flame converts them to O/Ne. The NS
formation would release ${\approx}10^{50}$ ergs into the remaining extended low
mass envelope. Using the STELLA radiative transfer code, we predict the
resulting optical light curves from these exploded envelopes. Reaching absolute
magnitudes of $M_V\approx -17$, these transients are bright for about one week,
and have many features of the class of luminous, rapidly evolving transients
studied by Drout and collaborators.
