We report the detection of a spectral signature observed at 682 cm$^{-1}$ by the Cassini Composite Infrared Spectrometer (CIRS) in nadir and limb geometry observations of Titans southern stratospheric polar region in the middle of southern fall, while stratospheric temperatures are the coldest since the beginning of the Cassini mission. The 682 cm$^{-1}$ signature, which is only observed below an altitude of 300-km, is at least partly attributed to the benzene (C$_6$H$_6$) ice $ u_{4}$ C-H bending mode. While we first observed it in CIRS nadir spectra of the southern polar region in early 2013, we focus here on the study of nadir data acquired in May 2013, which have a more favorable observation geometry. We derived the C$_6$H$_6$ ice mass mixing ratio in 5{deg}S latitude bins from the south pole to 65{deg}S and infer the C$_6$H$_6$ cloud top altitude to be located deeper with increasing distance from the pole. We additionally analyzed limb data acquired in March 2015, which were the first limb dataset available after the May 2013 nadir observation, in order to infer a vertical profile of its mass mixing ratio in the 0.1 - 1 mbar region (250 - 170 km). We derive an upper limit of $sim$1.5 $mu$m for the equivalent radius of pure C$_6$H$_6$ ice particles from the shape of the observed emission band. Several other unidentified signatures are observed near 687 and 702 cm$^{-1}$ and possibly 695 cm$^{-1}$, which could also be due to ice spectral signatures as they are observed in the deep stratosphere at pressure levels similar to the C$_6$H$_6$ ice ones. We could not reproduce these signatures with pure nitrile ice (HCN, HC$_3$N,CH$_3$CN, C$_2$H$_5$CN and C$_2$N$_2$) spectra available in the literature except the 695 cm$^{-1}$ feature that could possibly be due to C$_2$H$_3$CN ice.