Using the Chandra X-ray Observatory and the Rossi X-ray Timing Explorer , we have studied the black hole candidate ( BHC ) X-ray transient XTE J1650–500 near the end of its 2001-2002 outburst after its transition to the low-hard state at X-ray luminosities down to L = 1.5 \times 10 ^ { 34 } erg s ^ { -1 } ( 1-9 keV , assuming a source distance of 4 kpc ) . Our results include a characterization of the spectral and timing properties . At the lowest sampled luminosity , we used an 18 ks Chandra observation to measure the power spectrum at low frequencies . For the 3 epochs at which we obtained Chandra / RXTE observations , the 0.5-20 keV energy spectrum is consistent with a spectral model consisting of a power-law with interstellar absorption . We detect evolution in the power-law photon index from \Gamma = 1.66 \pm 0.05 to \Gamma = 1.93 \pm 0.13 ( 90 % confidence errors ) , indicating that the source softens at low luminosities . The power spectra are characterized by strong ( 20-35 % fractional rms ) band-limited noise , which we model as a zero-centered Lorentzian . Including results from an RXTE study of XTE J1650–500 near the transition to the low-hard state by Kalemci et al . ( 2003 ) , the half-width of the zero-centered Lorentzian ( roughly where the band-limited noise cuts off ) drops from 4 Hz at L = 7 \times 10 ^ { 36 } erg s ^ { -1 } ( 1-9 keV , absorbed ) to 0.067 \pm 0.007 Hz at L = 9 \times 10 ^ { 34 } erg s ^ { -1 } to 0.0035 \pm 0.0010 Hz at the lowest luminosity . While the spectral and timing parameters evolve with luminosity , it is notable that the general shapes of the energy and power spectra remain the same , indicating that the source stays in the low-hard state . This implies that the X-ray emitting region of the system likely keeps the same overall structure , while the luminosity changes by a factor of 470 . We discuss how these results may constrain theoretical black hole accretion models .