We study numerically a model for active suspensions of self-propelled repulsive particles, for which a stable phase separation into a dilute and a dense phase is observed. We exploit the fact that for nonsquare boxes a stable "slab" configuration is reached, in which interfaces align with the shorter box edge. Evaluating a recent proposal for an intensive active swimming pressure, we demonstrate that the excess stress within the interface separating both phases is negative. The occurrence of a negative tension together with stable phase separation is a genuine nonequilibrium effect that is rationalized in terms of a positive stiffness, the estimate of which agrees excellently with the numerical data. Our results challenge effective thermodynamic descriptions and mappings of active Brownian particles onto passive pair potentials with attractions.