To work, the image sensor has to have power applied to it. When the poser is turned off the image sensor quits working.
Many people don't know that the image sensor in a camera is not digital - It's an analog device.
Many P&S cameras don't have shutter curtains. Shutter speed is just turning the image sensor on and off.
Some DSLR cameras, like Nikon's D40 and D70, use both methods.
Up to the cameras x-sync speed of 1/200, which has both shutter curtains fully open, the shutter curtains control the shutter speed. At faster shutter speeds, which would be the slit Josh mentioned, the D40/D70 shutter curtains are left completely open and turning the image sensor on and off controls the exposure time. That's how those cameras can sync flash at speeds of 1/500 to 1/4000 -8000 without using Nikon's high speed sync system.
In todays DSLR's the front/first curtain drops down towards the bottom of the camera to start the exposure, and the rear/second curtain drops down towards the bottom of the camera to stop the exposure.
Both curtains then return to their starting position.
If burst mode is used, that same sequence happens repeatedly.
Jeffrey Friedl's Blog » Nikon D3 Shutter Release in Super Slow Motion