We propose a scheme for probing the structure of vibrating molecules with photoelectrons generated from ultrashort soft-x-ray pulses. As an example we analyze below-100-eV photoelectrons liberated from the S(2p) orbital of vibrating SF6 molecules to image very small structural changes of molecular vibration. In particular, photoionization cross sections and photoelectron angular distributions (PAD) at nonequilibrium geometries can be retrieved accurately with photoelectrons near the shape resonance at 13 eV. This is achieved with a pump-probe scheme, in which the symmetric stretch mode is first Raman excited predominantly by a relatively short laser pulse and then later probed at different time delays by a few-femtosecond soft-x-ray pulse with photon energy near 200 eV.