I have noticed that with some delta-sigma ADCs, e.g. MCP3550, they don't stop working and their specs don't degrade if you go a few mV below the GND rail - and why should they? The most that should happen is that input protection diodes might just about start getting turned on.
The reason I ask is because I want to measure voltages of a few hundred mV but they can also go below zero by up to 10mV.
It's a long story but I am combining the measurement of various sensors, with the measurement of thermocouples, and thermocouples can produce small negative voltages. Very small; even -270C produces only
-10mV.
Obviously there are other ways to get around this (e.g. lifting the whole sensor interface up by 10mV) but I am trying to keep things simple because I am trying to measure various other voltages :)