It is recommended to supply a voltage to the input pin so that the logic of the output is fixed. When determining output logic High or Low, set it arbitrarily on the assumption it may be shorted with the output peripheral circuit.
Operation outside of the common mode input voltage range is outside of the guaranteed electrical characteristics. In the case of an open collector comparator, as long as the supplied voltage at one of the input pins is within the common mode input range the comparator will operate normally. However, when the voltage supplied to both input terminals falls out of the common mode input range the output will be fixed at Low. But with the BA10393/BA10339, if an input voltage higher than the supply voltage is input there is a possibility of destruction due to breakdown voltage.Related Link：Technical Document
Please verify the graph of the Input Offset Voltage vs Common Mode Input Voltage Characteristics included in the datasheet. The point at which the input offset voltage suddenly changes becomes the actual value for the common mode input voltage range.
When reverse voltage is supplied to the supply and ground pins, current flows through the electrostatic protection diodes between the VCC (VDD) and VEE (VSS) pins, which can lead to current degradation and, ultimately, destruction.