  We study the unitary relaxation dynamics of disordered spin chains following
a sudden quench of the Hamiltonian. We give analytical arguments, corroborated
by specific numerical examples, to show that the existence of a stationary
state depends crucially on the spectral and localization properties of the
final Hamiltonian, and not on the initial state. We test these ideas on
integrable one-dimensional models of the Ising or XY class, but argue more
generally on their validity for more complex (nonintegrable) models.
