Open Drain pin not going to GND
There is a distinct possibility that there is some type of latchup going on inside the MCU when the STAT output pin OFF. Under this condition the bleed from the 5V USB source through the LED and into the input pin of the MCU is going to bias the input above the 3.3V VDD of the MCU. This illegal condition may be turning on some circuit that makes the input pin of the MCU suddenly source a lot of current when the STAT pin goes low. The high level of current overloads the STAT pin to the point that it can no longer drive to GND.

You could check this condition by putting a current meter in series with the input to the MCU.

This condition could be avoided by using an MCU that as 5V tolerant inputs. Some do and others do not.