Flatline
The term flatline is usually used to describe an electrical measurement that shows no activity and therefore when represented, shows a flat line instead of a moving one. It almost always refers to either a flatlined electrocardiogram, where the heart shows no electrical activity (the state is called asystole), or to a flat electroencephalogram, in which the brain shows no electrical activity (brain death). Both of those specific cases are involved in various definitions of death. Some consider one who has flatlined to have been clinically dead, regardless of their eventual resusication or lack thereof, whereas others insist that one is alive until the moment of brain-death. This is mostly used in the medical industry when a person's pulse has stopped, indicating a flat line on the heart monitor.
The title of the 1990 movie Flatliners refers to its characters' experiments with states of temporary near-clinical death.