A metastable state, or a false vacuum, is not an eigenstate of the Hamiltonian in quantum field theory. Its energy density has a non-zero imaginary part equal to its decay width. Therefore, supersymmetry cannot be exact in the false vacuum. We calculate the size of this effect using the path integral approach.
Kusenko, A. (1996). Supersymmetry in the false vacuum. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 377(4), 245–249. https://doi.org/10.1016/0370-2693(96)00405-4