Positive 12 volts is required to keep the run solenoid in your injection pump energized as has been mentioned. Remove the 12 volts and that solenoid springs closed and cuts the fuel which is the reason the engine shuts off when you turn the key off.
Also despite seeming counterintuitive, the voltage regulator in the newer type alternators requires 12 volt input from the battery at very low amperage for the regulator to operate. When you don't provide this 12 volts the alternator appears to not charge when tested on a voltmeter.
Because of these two things, the engine is not designed to be run with either battery terminal removed or with no battery at all.