Most dashcams will loop or roll through the memory. Video files are stored as intervals (length upon your choosing). When the cars becomes full, it starts deleting the oldest files first, one at a time. So depending on the card size, you will always have the last 2 hours available.
Some dashcams can stay on with the car off if there is constant power supply to it. They also can detect that the car is not running due to drop in voltage and run at a lower frame rate or quality to lengthen the amount of storage time. Some also will record only upon movement within the camera view or upon a shock.
These options are usually costly though, so most cheap to mid-range cams don't have them or don't work well if they do.
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