A decomposition of the non-equilibrium stationary state of a quadratic Fermi system influenced by linear baths is obtained and used to establish a simulation protocol in terms of tensor states. The scheme is then applied to examine the occurrence of uncoupled Majorana fermions in Kitaev chains subject to baths on the ends. The resulting phase diagram is compared against the topological characterization of the equilibrium chain and the protocol efficiency is studied with respect to this model