Is the engine supposed to turn off when you unplug the Mass airflow meter?

Normally, no. Doing so will be instantly detected by the Engine Computer. It will set a diagnostic fault code, then run the engine based on all the other sensor data. Most Engine Computers see the missing or "implausible" signal coming from the MAF sensor, then, after setting the appropriate fault code, go into a backup strategy where they "inject" an approximate value to run on. Engine performance and emissions will not be at their best, but the engine will run. The MAP sensor can be used to replace the MAF sensor's data. In fact, for a real long time Chrysler was the only manufacturer that never needed a MAF sensor. They used only the MAP sensor which measures intake manifold vacuum.

One problem with driving with the MAF sensor unplugged is the Engine Computer uses its signal voltages to compare to other sensors and operating conditions to determine when something is not working properly. With a fault code set, it knows the MAF sensor's readings can't be trusted, so it suspends any tests that rely on or use that missing data. That leaves a number of potential defects to go undetected. Some of those other defects can be relatively minor, but turn expensive if unwittingly ignored when you don't know about them. Since a MAF sensor defect can adversely affect emissions, a fault code related to it will turn on the Check Engine light. Even if a new problem does get detected, you'll never know because that light is already on. This again can allow a simple problem to turn into an expensive repair if ignored.

Is there more to this story, or are you just harvesting some of my wondrous knowledge?