We investigate static configurations of a vacuumless scalar field as ‘hair’ on a black hole. The vacuumless field has run-away behaviour, meaning the scalar potential vanishes only at infinite field strength, and is also responsible for a cosmic acceleration horizon. The classic no-hair theorems do not prevent the existence of static configurations, in the form of a spherical domain wall, trapped between the two horizons. We study the properties of such configurations and show that, although the configurations are ultimately unstable, long-lived solutions are possible. We make a perturbation study to estimate the instability time scale, which can be as large as 6 × 107 times the black hole crossing time. We identify classes of observers who can never observe the scalar field become unstable, because they pass beyond the cosmological event horizon in a time interval shorter than the instability time scale.