We show that hard encounters in the central regions of globular clusters embedded in dark matter (DM) haloes necessarily lead to the formation of gravitationally-bound stellar envelopes that extend far beyond the nominal tidal radius of the system. Using statistical arguments and numerical techniques we derive the equilibrium distribution function of stars ejected from the centre of a non-divergent spherical potential. Independently of the velocity distribution with which stars are ejected, GC envelopes have density profiles that approach asymptotically $rhosim r^{-4}$ at large distances and become isothermal towards the centre. Adding a DM halo component leaves two clear-cut observational signatures: (i) a flattening, or slightly increase of the projected velocity dispersion profile at large distances, and (ii) an outer surface density profile that is systematically shallower than in models with no dark matter.
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