In case of reverse voltage (negative source to positive terminal and vice versa) will blast the aluminum electrolytic capacitor due to the hydrogen ion theory. In this wrong wiring connection, there is positive voltage across the electrolytic cathode and the negative voltage appears across the oxide layer.
Most super capacitors (supercaps) can be discharged down to 0 V and recharged to their maximum voltage with the manufacturer recommended charge current. A simple voltage regulating LED driver with constant current, usually regulated by sensing a low side, series current sense resistor, then a voltage clamp can be used to charge a super capacitor.
Short version: the reversal ONLY occurs if the capacitor is connected to an inductor. The inductor-current cannot change rapidly, and this causes the voltage across the capacitor to, rather than just exponentially settling to zero, instead the voltage "overshoots" and becomes reversed.
Eventually, the super capacitor voltage, and therefore the charging circuit’s operating efficiency, increases so the capacitor charges at the desired constant (fast or max) charge current, ICHG, until it reaches and remains at constant voltage (CV) regulation voltage, VREG.
The damage inflicted on a capacitor by a transient voltage reversal is a nonlinear function of the degree of reversal. As shown in Figure 2, the change in life between 80 and 85 % reversal is much greater than the change between 20 and 30 % reversal.
So if you have applied a reversed voltage on a polar capacitor and using for hobbies projects, You must test and check the capacitor before placing in the circuit or replace with new one in case of commercial and industrial usage.