An input pin will read the state of a logic signal wired to it. If left unconnected (floating) it is not guaranteed at which state it will assume, and subject to switching with just circuit noise.
However if the internal software pull-up is activated for the pin then the input will assume a HIGH input value even if not wired to anything externally.
There is no software pull-down available so the only way to assure a low on a unwired input pin is to wire a resistor to ground from the pin.
Lefty