I have the question about ADG5208F.
Q.How does it work, if it has follow status?
Input = 5V
Signal = switch ON
D = GND
In this case, it connected for the OPAMP .
The customer want to not get the damage, when the OPAMP's voltage is GND level by supply voltage is shutdown.
The AD8613 has an absolute maximum rating for the input current of 10mA (page 5 of the data sheet).
You should limit the current through the input protection diodes to less than that.
This can be done very easily in your circuit by adding a series resistor between Dx and the input of the OPAMP.
10k Ohm would be a good value since the bias current of the OPAMP is only 780 pA worst case.
The added offset voltage generated by this would be far less than the offset of the OPAMP itself.