  We report on the detection of X-ray polarisation in the black-hole X-ray
binary Swift J1727.8$-$1613 during its dim hard spectral state by the Imaging
X-ray Polarimetry Explorer (IXPE). This is the first detection of X-ray
polarisation at the transition from the soft to the hard state in an X-ray
binary. We find an averaged 2$-$8 keV polarisation degree of (3.3 ${\pm}$ 0.4)
% and a corresponding polarisation angle of 3{\deg} ${\pm}$ 4{\deg}, which
matches the polarisation detected during the rising stage of the outburst, in
September$-$October 2023, within 1${\sigma}$ uncertainty. The observational
campaign complements previous studies of this source and enables comparison of
the X-ray polarisation properties of a single transient across the X-ray
hardness-intensity diagram. The complete recovery of the X-ray polarisation
properties, including the energy dependence, came after a dramatic drop in the
X-ray polarisation during the soft state. The new IXPE observations in the dim
hard state at the reverse transition indicate that the accretion properties,
including the geometry of the corona, appear to be strikingly similar to the
bright hard state during the outburst rise despite the X-ray luminosities
differing by two orders of magnitude.
