The energies of 2-quasiparticle (2-qp) states in heavy shell-stabilized nuclei provide information on the single-particle states that are responsible for the stability of superheavy nuclei. We have calculated the energies of 2-qp states in Rf256, which suggest that a long-lived, low-energy 8- isomer should exist. A search was conducted for this isomer through a calorimetric conversion electron signal, sandwiched in time between implantation of a Rf256 nucleus and its fission decay, all within the same pixel of a double-sided Si strip detector. A 17(5)-μs isomer was identified. However, its low population, ~5(2)% that of the ground state instead of the expected ~30%, suggests that it is more likely a 4-qp isomer. Possible reasons for the absence of an electromagnetic signature of a 2-qp isomer decay are discussed. These include the favored possibility that the isomer decays by fission, with a half-life indistinguishably close to that of the ground state. Another possibility, that there is no 2-qp isomer at all, would imply an abrupt termination of axially symmetric deformed shapes at Z=104, which describes nuclei with Z=92-103 very well
