LVTTL Buffer IC output logic when input is high and not connected to supply voltage
IC behaviour is usually unspecified when no power is supplied. As commented, you will try to power the whole board with your input signals in that case, due to the ESD protection diode.
There are, however special IC families that are are rated for this (for texas device look for the &quot;Ioff partial power down&quot; feature). Anyway I'd recommend at least a protection resistor on the inputs. Difficult to say more without the schematic.