Replacing an NE555 with a 74HC123D
Because the 123 has both positive and negative trigger inputs, it is possible to feed the output back to the input and create an oscillator.  However, it is not as simple as it might seem because the timing capacitor needs time to discharge between cycles.  The result is an oscillator circuit that is less accurate/precise/stable than a 555 circuit.

Your question is comparing apples and oranges.  HC stands for High-speed CMOS, while a 555 (without any prefix) is assumed to be the original, bipolar design.  If you compare the datasheet static or standby current values for a bipolar NE555 and a CMOS LMC555N, you will see that the standby current values are much lower for the CMOS part.

Checking some datasheets, I see that the HC123 has a max operating current of 80 mA, while the LMC555 comes in at around 100 uA typical and 250 uA max. at 5 V.  Given the difference in part size and cost, and circuit complexity, how badly do you need the lower operating current?