  Soft X-rays high resolution spectroscopy of obscured AGNs shows the existence
of a complex soft $X$-ray spectrum dominated by emission lines of He and H-like
transitions of elements from Carbon to Neon, as well as L-shell transitions due
to iron ions. In this paper we characterize the XMM-Newton RGS spectrum of the
Seyfert 1 galaxy NGC 4051 observed during a low flux state and infer the
physical properties of the emitting and absorbing gas in the soft X-ray regime.
X-ray high-resolution spectroscopy offers a powerful diagnostic tool since the
observed spectral features strongly depend on the physical properties of matter
(ionization parameter U, electron density n_e, hydrogen column density N_H),
which in turn are tightly related to the location and size of the X-ray
emitting clouds. We carried out a phenomenological study to identify the atomic
transitions detected in the spectra. This study suggests that the spectrum is
dominated by emission from a photoionised plasma. Then, we used the
photoionization code Cloudy to produce synthetic models for the emission line
component and the warm absorber observed during phases of high intrinsic
luminosity. The low state spectrum cannot be described by a single
photoionization component. A multi-ionization phase gas with ionization
parameter in the range log U = 0.63-1.90 and column density log N_H =
22.10-22.72 cm^-2 is required, while the electron density n_e remains
unconstrained. A warm absorber medium is required by the fit with parameters
log U = 0.85, log N_H = 23.40 and log n_e \ut< 5. The model is consistent with
an X-ray emitting regions at a distance > 5 x 10^-2 pc from the central engine.
