If the Arduino is powered down, zero volts goes to the BJT base. The BJT is off, so the gate of the MOSFET is at 3.7V, same as the Source pin. Therefore the MOSFET is Off when the Arduino does not have power.
If the Arduino is powered down, zero volts goes to the BJT base. The BJT is off, so the gate of the MOSFET is at 3.7V, same as the Source pin. Therefore the MOSFET is Off when the Arduino does not have power.