Op-Amp output if supply voltage is zero
Basically all opamps I know ( mostly precision parts with GBW product smaller than 100 MHz) have overvoltage clamping diodes at the inputs. (I am not sure but maybe these are inevitable parasitic diodes.) When you push/pull current through an input of an unpowered opamp, these diodes will conduct the charge to the positive supply or from the negative supply.
Usually these diodes arent rated for a lot of current though (mAs). If the supplies are shorted both to GND, then you will just dump this charge into GND.
If you have actual supplies connected (though unpowered) and if you push enough current into the supplies, the opamp will eventually turn on and run off this current. However, to maintain this situation and keep the opamp powered, the input has to stick beyond the rail. Therefore, a likely output is positive/negative limit at the instantaneous supply voltage of the opamp.
If you push more current than the opamp needs to run and maintain its output, the supply voltage will rise until something gives way and blows up.