Power factor can be described in the frequency domain. Recall that the power measurements are the same for the integrals of voltage and current in either time or frequency. For frequency, two things could make the power factor 0. The first is the common definition -- that phase = +-90d between voltage and current. The second occurs when voltage and current occur at different frequencies. This can be "harmonic power factor", or any number of different descriptions.
For example, a DC source that connects to an AC current sink. The average power is 0, but measuring voltage and current will give non-zero RMS values and thus some apparent power. The source/load isn't inductive or capacitive as there is no meaningful phase that can be measured. Another common example would be the diode-capacitor AC-DC converters. These draw current in large bursts of current at the peak of the voltage waveform. The peak is near the center of the voltage waveform, so it will be mostly resistive. But the RMS current is very high. The power factor is low despite the apparent resistive load because the current waveform has lots of energy in frequencies other than the fundamental
For the original question, inductive loads at 0 PF have no resistance. They would simply charge and discharge each cycle with current exactly 90deg different than voltage. For a 0 PF resistive load, you could have something like the diode-capacitor example, but to the extreme -- where current is very short, very high bursts only at the peak of the sine wave. The load will be resistive, but will approach a 0 PF as the pulse width is decreased. (in this case, V*I has a positive average, and V*I is never negative, so energy is only transfered to the load.)