Remembering way back in late 2015, the P3P had issues with falling out of the sky on low battery. This was most prevalent when starting a new flight on a partial charge battery, and in cold flight condition. This occurred when the weakest of the 4 cells reached 3.0V. The P3P has a very small tolerance for landing. Correct me if I'm wrong, but for P3P 20% was around 3.3V. When that low it's always dangerous when giving the craft full throttle ASCEND and FORWARD. In fact, in the 1.6 firmware DJI actually built in a THROTTLE REDUCTION governor to prevent this mistake. In firmware 1.5 (this is old 2015 firmware) the craft didn't have the governor in the firmware, and craft were falling out of the sky, especially in cold weather where batteries don't do so good.
In the P3P I think they ALWAYS had the issue of motor shut down if the craft got to 2.99V, which likely happened to the OP. It's really helpful if P3P flyers always display the voltage on the screen, which is the real time voltage level of the weakest battery. If you start getting down to 3.2V, you should gingerly operate the throttle, however simply planning to land by 20% is the best way to avoid craft that drop from the sky.
Newer craft, such as Mavic2 (not sure about
P4P or MP), don't shut down the motors anymore at 2.99V. When the battery reaches 3.0V, it simply starts descending where ever it's at. On
M2 this 3.0V level occurs after 0% on the bar gauge, so you can actually continue to maintain altitude and move forward for about a minute after 0%, but it's not advised of course. But once it reaches 3.0V on the weakest cell, it will slowly descend uncontrollably. Newer DJI craft won't simply turn off the motors and fall form the sky like P3P, this motor shutdown flaw, exhibited in P3P has been fixed in newer craft. DJI will never admit to this flaw in the P3P, but I deem it as a serious P3P flaw, one that I don't think ever got fixed, entirely. They only included the governor in firmware 1.6 and later firmware, which is more like a bandaid than a fix.
As newer craft were released, you will notice the tolerance to accidental low battery level is greater. When landing
M2P for instance, if my memory is correct, I believe 20% is ~3.5V instead of 3.3V in the P3P (correct me if I'm wrong). This gives more margin for error, more mileage to return when mistakes are made.