  We present high-resolution VLT/UVES spectroscopy and a detailed analysis of
the unique Broad Absorption-Line system towards the quasar SDSS
J165252.67+265001.96. This system exhibits low-ionization metal absorption
lines from the ground states and excited energy levels of Fe II and Mn II, and
the meta-stable 2^3S excited state of He I. The extended kinematics of the
absorber encompasses three main clumps with velocity offsets of -5680, -4550,
and -1770 km s$^{-1}$ from the quasar emission redshift, $z=0.3509\pm0.0003$,
derived from [O II] emission. Each clump shows moderate partial covering of the
background continuum source, $C_f \approx [0.53; 0.24; 0.81]$. We discuss the
excitation mechanisms at play in the gas, which we use to constrain the
distance of the clouds from the Active Galactic Nucleus (AGN) as well as the
density, temperature, and typical sizes of the clouds. The number density is
found to be $n_{\rm H} \sim 10^4\rm cm^{-3}$ and the temperature $T_e \sim
10^4\rm\,K$, with longitudinal cloudlet sizes of $\gtrsim0.01$ pc. Cloudy
photo-ionization modelling of He I$^{*}$, which is also produced at the
interface between the neutral and ionized phases, assuming the number densities
derived from Fe II, constrains the ionization parameter to be $\log U \sim -3$.
This corresponds to distances of a few 100 pc from the AGN. We discuss these
results in the more general context of associated absorption-line systems and
propose a connection between FeLoBALs and the recently-identified
molecular-rich intrinsic absorbers. Studies of significant samples of FeLoBALs,
even though rare per se, will soon be possible thanks to large dedicated
surveys paired with high-resolution spectroscopic follow-ups.
