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When switched off, a charged capacitor can still provide a current to the Base of a Bipolar Junction Transistor (BJT) through a resistor. But that current quickly lowers over time. The current goes down as the capacitor discharges, which means that it’s voltage is lowering. Therefore the BJT will allow less and less current to flow through a load connected to the Collector.
The Collector to Emitter (and series load) passes many times the amount current as what is flowing through the Base. Probably 200 to 300 as much current. So, an LED can stay fully lit for a short period of time, and then as the capacitor runs out of stored charge, the Base current will lower down towards zero milliamps of current, as will the collector current.
Once the Collector limits current to less than the maximum current that the LED and it’s protective resistor will pass, then the current through the LED will be set by bow much current the Collector lets pass through. Less current, equals a dimmer LED.
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