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The origins of type Ia supernovae (SNe Ia) are still debated. Some of the leading scenarios involve a double detonation in double white dwarf (WD) systems. In these scenarios, helium shell detonation occurs on top of a carbon-oxygen (CO) WD, which then drives the detonation of the CO-core, producing a SN Ia. Extensive studies have been done on the possibility of a double helium detonation, following a dynamical helium mass-transfer phase onto a CO-WD. However, 3D self-consistent modeling of the double-WD system, the mass transfer, and the helium shell detonation have been little studied. Here we use 3D hydrodynamical simulations to explore this case in which a helium detonation occurs near the point of Roche lobe overflow of the donor WD and may lead to an SN Ia through the dynamically driven double-degenerate double-detonation (D6) mechanism. We find that the helium layer of the accreting primary WD does undergo a detonation, while the underlying carbon-oxygen core does not, leading to an extremely rapid and faint nova-like transient instead of a luminous SN Ia event. This failed core detonation suggests that D6 SNe Ia may be restricted to the most massive carbon-oxygen primary WDs. We highlight the nucleosynthesis of the long-lived radioisotope $^{44}$Ti during explosive helium burning, which may serve as a hallmark both of successful as well as failed D6 events which subsequently detonate as classical double-degenerate mergers., Comment: 11 pages, 4 figures, 1 table. Published in the Astrophysical Journal Letters