Diode capacitor circuit, what is the output across the diode?
In the original posted question, the explanation until "Vout = Vin + 10" is all right.
V_C_right - V_C_left = 10V all the time after t=0+.
Vin, or say V_C_left, will be driven in sinusoidal form from -10V to 10V all the time.
Accordingly, Vout, or say V_C_right, will be in sinusoidal form from 0V to 20V all the time, with Vout - Vin = 10Vdc, or say V_C_right - V_C_left = 10Vdc all the time.
Neither Vin or Vout gets ever stuck at 0V.