We present a detailed spectral analysis of the X1.3 flare of 2005 January 19 using hard X-ray (HXR) spectra obtained with RHESSI. This flare exhibits HXR pulses during the impulsive phase, with a particularly pronounced peak at the end of the impulsive phase. This peak is associated with HXR emission up to high energies (>300 keV) but does not show any Neupert effect (i.e., no simultaneous rise in soft X-rays). Fitting the spatially integrated photon spectra with a Maxwellian plus a nonthermal thick-target component reveals that the data are consistent with a high low-energy cutoff ( 100 keV) of the energetic electrons during the late peak. The high low-energy cutoff straightforwardly explains the lack of a Neupert effect—while highly energetic electrons are produced efficiently, there is a lack of low-energy electrons that usually contain the bulk of the total energy. Hence, the energy input into the chromosphere remains too small to trigger chromospheric evaporation. This observation shows that the characteristics of electron acceleration can change dramatically and rapidly at the end of the impulsive phase of solar flares. This could be evidence for physically distinct acceleration processes acting in the same event, or alternatively for a sudden shift in the characteristic parameters of the accelerator. Using radio observations and comparing HXR images with magnetograms, we conclude that changes in the strength and the topology of the magnetic field in which the accelerator is working are responsible for the profound changes in the injected electron spectrum.