What would cause a voltage rail to be held low without measuring a short circuit?
You are experiencing a phenomenon where ESD voltage spikes enter your IC chip and cause one of two things to happen:


Stray PNPN junctions on the silicon can latch up like an SCR and can cause massive current to flow where it is not intended and thus cause fusing and melt damage of the silicon.
The voltage spike being high can also cause insulation layers on the chip to be punched through and create direct circuit shorts. These shorts can cause circuit malfunction or even outright silicon damage.


Note it is all too common that ESD damage to ICs cannot be measured with a typical ohms measurement with a DMM because the meter applies just a low voltage to the test connections. However when the chip attempts to power up the supply will get high enough to exceed some threshold for the silicon chip to startup. Once damaged circuitry attempts to operate it can cause the voltage rail clamping that you see. You may want to use an oscilloscope to capture the initial rise of your 1.8V supply and you may very well see it rise up to a little over 1.0V -> 1.2V before it then gets pulled quickly down to near ground.

I suspect that your 1.8V supply has current limiting on it. In this case that is a good thing because without it you would likely be seeing burnout smoke holes in the top of these chips.