Let us say that we have the following negative clamper circuit with a 50 volt peak-to-peak square wave as an input:
The output from the circuit is a -50 volt square wave with the peak positive point referenced to 0 volts.
I want an accurate interpretation of the output voltage. As far as I understand at $T_o$, the -25 v appears across the diode and resistor. When the voltage drop across $C$ reaches -25 volts, the value of the output is 0 volts. At $T_1$, the -25 volts input signal and -25 volts signal on the $C$ are in series which explains why we see the -50 volts appearing across the resistor and diode. This is how I've made sense of the output voltage so far.