Depending on the battery capacity and age, 5% remaining can mean "I'm dead, and don't have enough charge left to spin up the disk" or "2 hours remaining." In the first situation, it's too late to salvage the recording. In the second situation, there's 2 hours left and the user could miss something important because the player stops early to shut down. So while it sounds like a good idea, due to the nature of batteries it's just not very feasible that the player could make a useful judgment consistently enough to not anger people one way or another.
Meanwhile, the .wav file you get can be recovered. I believe it's just a .wav file missing the headers, so if it's opened as raw audio and you tell the program the right values it should be usable.