  We present the observations of a weak MgII absorption system detected at
z~0.452 in the UVES high resolution spectrum of the QSO HE0001-2340. The weaker
of the two MgII components forming the system shows associated absorptions due
to SiI, CaI and FeI observed for the first time in a QSO spectrum. We
investigate the nature of this absorber by comparing its properties with those
of different classes of absorbers (weak MgII, Damped Ly-alpha systems and local
interstellar clouds) and reproducing its ionization conditions with
photoionization models. The observed absorber belongs to the class of weak MgII
systems on the basis of its equivalent width, however the relative strength of
commonly observed transitions deviates significantly from those of the above
mentioned absorbers. A rough estimate of the probability to cross such a system
with a QSO line of sight is P~0.03. The presence of rare neutral transitions
suggests that the cloud is shielded by a large amount of neutral hydrogen. A
detailed comparison of the observed column densities with the average
properties of damped Ly-alpha systems and local interstellar cold clouds shows,
in particular, deficient MgII/MgI and CaII/CaI ratios in our cloud. The results
of photoionization models indicate that the cloud could be ionized by the UV
background. However, a simple model of a single cloud with uniform density
cannot reproduce the observed ionic abundance ratios, suggesting a more complex
density structure for the absorber. Supposing that ionization corrections are
negligible, the most puzzling result is the underabundance of magnesium with
respect to iron which is hard to explain both with nucleosynthesis and with
differential dust depletion. [Abridged]
