Liquid crystalline elastomers combine the ordering properties of liquid crystals with elasticity of crosslinked polymer networks. In monodomain (permanently aligned) elastomers, altering the orientational (nematic) order causes changes in the equilibrium sample length, which is the basis of the famous effect of large-amplitude reversible mechanical actuation. The stimulus for this effect could be a change in temperature, or illumination by light in photosensitized elastomers, but equally the nematic order changes by mixing with a solvent. This work theoretically investigates a competition between the spontaneous contraction on swelling of a monodomain nematic elastomer and the externally imposed stretching. We find that this competition leads to bistability in the system and allows a two-phase separation between a nematic state with lower swelling and an isotropic state with higher solvent concentration. We calculated the conditions in which the instability occurs as well as the mechanical and geometric parameters of equilibrium states. Being able to predict how this instability arises will provide opportunities for exploiting nematic elastomer filaments.