When power removed from LED circuit LED stays on
I have a 12 V DC input that I am stepping down to 2 V with 610 ohm resistor. When power is removed the light is staying on for a period of time and slowly dims.


I suspect that you mean when you switch off the mains power that the LED fades out.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. An old-fashioned power supply driving an LED.

How it works:


SW1 switches the power on and off.
XFMR1 is a transformer and steps the voltage down from mains to the low voltage required - probably about 9 V AC in your case.
BR1 is a bridge rectifier consisting of four diodes. No matter what the polarity of the input voltage on the ~ ~ terminals the voltage is "rectified" and current always comes out on the + terminal. The bridge rectifier will output pulses of current at the peaks of the alternating voltage.
C1 is the smoothing capacitor which stores some charge between pulses from BR1.
R1 limits the current to the LED to a safe value.
D1, the LED, will have a certain "forward voltage", Vf, at the current set by R1. 



  Would the resistor be acting like a battery?


Definitely not. The fading effect is caused by the charge stored in C1 slowly bleeding out through R1 - D1.