We propose a simple model explaining two outstanding astrophysical problems related to compact objects: (1) that of stars such as G87−7 (alias EG 50) that constitute a class of relatively low-mass white dwarfs which nevertheless fall away from the C/O composition and (2) that of GRB 110328A/Swift J164449.3+57345 which showed spectacularly long-lived strong X-ray flaring, posing a challenge to standard GRB models. We argue that both these observations may have an explanation within the unified framework of a Quark-Nova occurring in a low-mass X-ray binary (neutron starwhite dwarf). For LMXBs where the binary separation is sufficiently tight, ejecta from the exploding Neutron Star triggers nuclear burning in the white dwarf on impact, possibly leading to Fe-rich composition compact white dwarfs with mass 0.43M ⊙ < M WD < 0.72M ⊙ , reminiscent of G87−7. Our results rely on the assumption, which ultimately needs to be tested by hydrodynamic and nucleosynthesis simulations, that under certain circumstances the WD can avoid the thermonuclear runaway. For heavier white dwarfs (i.e. M WD > 0.72M ⊙ ) experiencing the QN shock, degeneracy will not be lifted when Carbon burning begins, and a sub-Chandrasekhar Type Ia Supernovae may result in our model. Under slightly different conditions, and for pure He white dwarfs (i.e. M WD < 0.43M ⊙ ), the white dwarf is ablated and its ashes raining down on the Quark star leads to accretion-driven X-ray luminosity with energetics and duration reminiscent of GRB 110328A. We predict additional flaring activity towards the end of the accretion phase if the Quark star turns into a Black Hole.