During its sungrazing perihelion passage, comet ISON appeared in the field of view of the SUMER spectrometer and allowed unique observations at far-ultraviolet wavelengths with high spatial and temporal resolution. We report results of these observations completed on November 28, 2013, when the comet was only 2.82 R_Sun away from the Sun. Our data show the arrow-shaped dust tail in Ly-$alpha$ emission trailing behind the predicted position of the nucleus, but offset from the trajectory. We interpret the emission as sunlight that is scattered at micron-sized dust particles. We modeled the dust emission and dynamics to reproduce the appearance of the tail. We were unable to detect any signature of cometary gas or plasma around the expected position of the nucleus and conclude that the outgassing processes must have stopped before the observation started. Moreover, the model we used to reproduce the observed dust tail needs a sharp fall-off of the dust production hours before perihelion transit. We compare the radiances of the disk and the dust tail for an estimate of the dust column density and tail mass.
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