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LMV321: LMV321 Input voltage range when unpowered

Part Number: LMV321
Other Parts Discussed in Thread: LM321LV, TLV9001

I would like to use a small single opamp as a buffer monitoring battery input for a signal, the power is supplied by uC output pin, so is 3.3V,  the device will be powered off most of the time to reduce energy.

When this happens the input will float (through large resistor) to the battery voltage, which can be 4.2V or 12V.  This is within the acceptable range of the opamp input, but maybe not when not powered up nor if greater than Vcc.

Is there any way to tell what the behavior of this or an alternative opamp is in this situation?  Is there a rail-rail op amp that would do this?  Apologies if the datasheet states this.