let's say i have a circuit like this: V+ - pullup resistor - switch - GND, and between the resistor and the switch i have a connection to a given component (e.g. an IC's pin), which i'm calling A (not much fantasy here).
if the switch is closed (on), the circuit is closed, and A receives V+ volts... but if the current is reduced by the resistor, then the current is minimal. if the voltage is 5 V and the resistor is 10K, it'd get just 0.5 mA! (something's not clear here)
if the switch is open (off), the circuit is still closed even if it's not connected to the ground (right because the circuit is open). even if A has a ground-level voltage (with potential drop between V+ and A the same as V+, ie. with A = ground), the current is minimal (the famous 0.5 mA) which could be assumed to be 0.. or not?