Abstract Recent observations of the stellar halo have uncovered the debris of an ancient merger, Gaia–Sausage–Enceladus (GSE), estimated to have occurred ≳8 Gyr ago. Follow-up studies have associated GSE with a large-scale tilt in the stellar halo that links two well-known stellar overdensities in diagonally opposing octants of the Galaxy (the Hercules–Aquila Cloud and Virgo Overdensity; HAC and VOD). In this paper, we study the plausibility of such unmixed merger debris persisting over several gigayears in the Galactic halo. We employ the simulated stellar halo from Naidu et al., which reproduces several key properties of the merger remnant, including the large-scale tilt. By integrating the orbits of these simulated stellar halo particles, we show that adoption of a spherical halo potential results in rapid phase mixing of the asymmetry. However, adopting a tilted halo potential preserves the initial asymmetry in the stellar halo for many gigayears. The asymmetry is preserved even when a realistic growing disk is added to the potential. These results suggest that HAC and VOD are long-lived structures that are associated with GSE and that the dark matter halo of the Galaxy is tilted with respect to the disk and aligned in the direction of HAC–VOD. Such halo–disk misalignment is common in modern cosmological simulations. Lastly, we study the relationship between the local and global stellar halo in light of a tilted global halo comprised of highly radial orbits. We find that the local halo offers a dynamically biased view of the global halo due to its displacement from the Galactic center.