  We use a random pinning procedure to investigate stable glassy states
associated with large deviations of the activity in a model glass-former. We
pin particles both from active (equilibrium) configurations and from stable
(inactive) glassy states. By comparing the distribution of the overlap between
states that share pinned particles, we infer that the inactive states are
characterised by a structural length scale that is comparable with the system
size. This is a manifestation of amorphous order in these glassy states, which
helps to explain their stability.
