  We examine the sensitivity at a future 100 TeV proton-proton collider to
compressed dark sectors whose decay products are invisible due to
below-threshold energies and/or small couplings to the Standard Model. This
scenario could be relevant to models of WIMP dark matter, where the lightest
New Physics state is an (isolated) electroweak multiplet whose lowest component
is stable on cosmological timescales. We rely on the additional emission of a
hard on-shell $Z$-boson decaying to leptons, a channel with low background
systematics, and include a careful estimate of the real and fake backgrounds to
this process in our analysis. We show that an integrated luminosity of 30
ab$^{-1}$ would allow exclusion of a TeV-scale compressed dark sector with
inclusive production cross section of 0.3 fb, for 1\% background systematic
uncertainty and splittings below 5 GeV. This translates to exclusion of a pure
higgsino (wino) multiplet with mass of 500 (970) GeV.
