Consider the following circuit.
The output wave form will look like this
Orange - input signal Blue - output signal
The Wikipedia entry on Electrolytic capacitors says
Nevertheless, electrolytic capacitors can withstand for short instants a reverse voltage for a limited number of cycles. In detail aluminum electrolytic capacitors with non-solid electrolyte can withstand a reverse voltage of about 1 V to 1.5 V. This reverse voltage should never be used to determine the maximum reverse voltage under which a capacitor can be used permanently
It does not specify what a short duration is.
Since polarized capacitors are meant to be used one way, will the falling edge's dv/dt damage the capacitor ?