Running chip at low voltage

Hi,
for my experiment powered by 2 AAAs (around 2.6V) I need multiplexer. Only mux I have is CD4051 with recomended operating range 3-20 V. I tried to use it anyway until I get 74HC4051 with voltage range 2-6V. It seems to work flawlessly. I noticed before chips work at lower voltage than rated seemingly without problems. I know chips may work wrong when voltage is too low. For CPUs it may execute wrong code, outputs are weak, inputs may read logic levels wrong etc. But is there possibility for damage if possible faulty behavior is no problem? What I mean - too low voltage means FET does not open fully possibly damaging it if it is switching a lot of power. But if the mux is multiplexing only signals with high impedance nothing bad would happen even if all were shorted together. As well no damage can happen even if the channnel stays closed - I would only get wrong reading.
So is it OK to use the mux with lower voltage (as proof of concept until I get the right one) or is there a risk it will get damaged somehow?

No risk of damage - it just won't conduct very well or linearly when supposed to be on. The datasheet
shows the behaviour at several different supply voltages, you can extrapolate from that perhaps.

What will damage it is signal voltages straying outside of the supply voltage range, a big no-no for every
CMOS chip.

Smajdalf:
well no damage can happen even if the channnel stays closed - I would only get wrong reading.

Right. Also you need control lines of the MUX be at the same voltage as IC, common arduino is 5V powered device, and it implies using level converters

Why does it have to be two batteries , use something else - you may find your circuit unreliable at lower voltages ( eg stops working on a hot day )