We present here results obtained from a detailed timing and spectral analysis of three BeppoSAX observations of the binary X-ray pulsar GX 1+4 carried out in 1996 August, 1997 March, and 2000 August. In the middle of the 2000 August observation, the source was in a rare low-intensity state that lasted for about 30 hr. Although the source does not show pulsations in the soft X-ray band (1.0-5.5 keV) during the extended low state, pulsations are detected in the 5.5-10.0 keV energy band of the MECS detector and in the hard X-ray energy bands (15-150 keV) of the PDS instrument. Comparing the 2-10 keV flux during this low state with the previously reported low states in GX 1+4, we suggest that the propeller regime in GX 1+4 occurs at a lower mass accretion rate than reported earlier. Broadband (1.0-150 keV) pulse-averaged spectroscopy reveals that the best-fit model comprises a Comptonized continuum along with an iron Kalpha emission line. A strong iron Kbeta emission line is detected for the first time in GX 1+4 during the extended low state of the 2000 observation with an equivalent width of similar to550 eV. The optical depth and temperature of the Comptonizing plasma are found to be identical during the high- and low-intensity states, whereas the hydrogen column density and the temperature of the seed photons are higher during the low state. We also present results from pulse-phase-resolved spectroscopy during the high- and low-flux episodes.