battery drain rate when half batteries are empty
Alkaline cells have essentially no energy at about 0.8V. This means that 4 cells would be about 6V at full and 3.2V at empty. "Low battery" is usually about 1V or so. This means that the device would be supplied with about 4.1V total. This represents about 35% full.

The next hurdle is that all four cells will keep discharging, and once they hit 0.8V they rapidly crash down to 0V. This means that the supply voltage will suddenly drop to below 3V. There is no guarantee that the device will continue working with such a low voltage, and if it did, there is also no guarantee that the good cells can force enough current through the dead cells to keep the device running.

And now the next bit of bad news. Since current is being forced through now completely dead cells, they can take on a reversed polarity. This can lead to physical damage of the battery, including but not limited to leakage of corrosive material.