  We demonstrate that the evolution of wall-like inhomogeneities in run-away
potentials, characteristic of dynamical supersymmetry breaking and moduli
stabilisation, is very similar to the evolution of domain wall networks
associated with double well potentials. Instabilities that would lead to a
rapid decay of domain walls can be significantly ameliorated by compensation
effects between a non-degeneracy of the vacua and a biased initial
distribution, which can be naturally expected in a wide class or particle
physics models that lead to out-of-equilibrium phase transitions. Within this
framework, it is possible to obtain domain walls that live long enough to be
relevant for the cosmic power spectrum and galaxy clustering, while being
compatible with the observed cosmic microwave background anisotropies.
