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The input is "floating" and act as a capacitor with low leakage. It is impossible to say if it will be high or low.
For the older 7404 and 74LS04 families, an unconnected input is high, so the output would be low.
An open 74HC very high input impedance input might easily be destroyed by static electricity or it might pickup radio or mains signals. If the input voltage floats at near half the supply voltage then the output will be linear conducting a fairly high current that will overheat and destroy the IC.
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