  A gapped ground state of a quantum spin system has a natural length scale set
by the gap. This length scale governs the decay of correlations. A common
intuition is that this length scale also controls the spatial relaxation
towards the ground state away from impurities or boundaries. The aim of this
article is to take a step towards a proof of this intuition. We assume that the
ground state is frustration-free and invertible, i.e.\ it has no long-range
entanglement. Moreover, we assume the property that we are aiming to prove for
one specific kind of boundary condition; namely open boundary conditions. This
assumption is also known as the "local topological quantum order" (LTQO)
condition. With these assumptions we can prove stretched exponential decay away
from boundaries or impurities, for any of the ground states of the perturbed
system. In contrast to most earlier results, we do not assume that the
perturbations at the boundary or the impurity are small. In particular, the
perturbed system itself can have long-range entanglement.
