  Recent observations of the stellar halo have uncovered the debris of an
ancient merger, Gaia-Sausage-Enceladus, 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 over-densities 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 Gyr in the Galactic halo. We employ the simulated
stellar halo from Naidu et al. (2021), 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 Gyr. 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.
