In theory, yes. And it does, when the battery voltage decreases gradually. The full charge is about 4.3V, empty about 3.2V. When the voltage gets to 3.5V, the OS starts crying for help. The exact numbers may differ slightly but you get the picture.

Unfortunately, with old batteries, you can easily have something like 4.2V which looks like an almost fully charged battery. But add some load, such as receive a call, and the voltage drops unexpectedly below 3V, or even below 2V. This is not only below the "empty" threshold, it is way below the lowest operating voltage of the CPU. To all intents and purposes, it looks to the CPU as if the battery has been pulled out. There is nothing it can do.