The datasheet for the LM317 says that its absolute maximum allowed input-output voltage differential is +40V, -0.3V. Then you should never allow the output voltage to be more than 0.3V higher than its input voltage.
They say, "When an output capacitor is connected to a regulator and the input is shorted, the output capacitor will discharge into the output of the regulator. ....this discharge path is through a large junction that is able to sustain 15A surge with no problem."
They say when a high value capacitor is added to the output then a diode should pass its very high discharge current to avoid damaging the LM317.
Why are you feeding a voltage to the output of the Li-Po battery cell that is higher than its charged voltage? You charge a Li-Po cell from a limited current then the cell's voltage slowly rises to a limit of 4.20V. The protection circuit does not protect the cell from feeding a voltage backwards to its output. The protection circuit limits the charging current then limits the maximum charging voltage to 4.20V, similar to a Li-Po charger circuit.
Don't you know that a Li-Po cell voltage averages 3.7V? Its actual voltages are 4.20V when it is fully charged, then as it discharges its voltage passes through its average of 3.7V, then continuing a discharge its voltage slowly drops to 3.2V when it should have its load disconnected. When a cell that is 3.2V is charged, then the charger feeds it a limited current and its voltage slowly rises. You never charge it from 4.2V at many Amps.
A Chinese company sells a photo of a protection circuit to Li-Po battery manufacturers. The photo is identical to an actual protection circuit, it is discussed and shown on You Tube. The "protected" battery cell you bought might have the fake protection circuit. Is that what you are testing for?