Videos from cameras are (typically) not corrupted by sudden power loss while writing. I say typically because some cameras do actively encode video. When being encode video is typically all looked at as one file and is compressed to fit certain boundaries. Though encoding is only useful in cameras where retaining many videos is important and space is an issue (cell phones, handheld video cams to take family movies). CCTV cams and dash cams aren't like this - though I'm not entirely sure about the ones in police cruisers. These types of cameras usually have a set duration to keep videos and will typically begin overwriting at that time limit or when the camera is full. These cameras don't encode because they generally have lower resolutions or giant storage space to keep up with the demand of video. When a camera doesn't have to encode it can write the file straight to disk. Meaning as soon as the camera records something, it's on the disk with the only lag time being how fast the storage can write. If a camera uses native format and writes constantly then there is nothing to corrupt. The camera stops dealing with that part of the file and moves along. When power is cut the camera simply stops and the file is complete. A good example would be a dvr from a CCTV setup. I can get the stream on my computer from anywhere in the world and see what's happening right that second or I can rewind 1 minute (same file) and I can view it bc the camera doesn't need that part of the file for anything, its done with it. If my employee walks up to the dvr and pulls the power cord it won't do anything(to the file specifically, as pulling power on a disk drive could ruin the entire drive.
Sorry for the long explanation.
But anyway it is true that if the car lost power due to an accident or a police asking you to turn off the vehicle the camera would stop recording and likely the reason they included it.