  The Milky Way's stellar halo, which extends to $>100$ kpc, encodes the
evolutionary history of our Galaxy. However, most studies of the halo to date
have been limited to within a few kpc of the Sun. Here, we characterize
differences between this local halo and the stellar halo in its entirety. We
construct a composite stellar halo model by combining observationally motivated
N-body simulations of the Milky Way's nine most massive disrupted dwarf
galaxies that account for almost all of the mass in the halo. We find that (1)
the representation by mass of different dwarf galaxies in the local halo
compared to the whole halo can be significantly overestimated (e.g., the Helmi
Streams) or underestimated (e.g., Cetus) and (2) properties of the overall halo
(e.g., net rotation) inferred via orbit integration of local halo stars are
significantly biased, because e.g., highly retrograde debris from
Gaia-Sausage-Enceladus is missing from the local halo. Therefore,
extrapolations from the local to the global halo should be treated with
caution. From analysis of a sample of 11 MW-like simulated halos, we identify a
population of recently accreted ($\lesssim5$ Gyrs) and disrupted galaxies on
high angular momenta orbits that are entirely missing from local samples, and
awaiting discovery in the outer halo. Our results motivate the need for surveys
of halo stars extending to the Galaxy's virial radius.
