I mentioned backdrive in a post above--then realized not everyone would know what I meant.
Techie version of explanation:
Backdrive = where an input all of a sudden acts as a weak output, or an output suddenly acts as a weak input (this can happen deeper inside the chip too--more on this below). This is due to voltage mismatches between what the transistors inside the chip are using as power and what they see as signal inputs. If you undervolt, you are getting closer and closer to the point where backdrive occurs.
How is this a bad thing? To be blunt, you can break your toys, gentlemen.
Two effects can occur--1) something called an "SCR" effect, and 2) parasitic diode drive. Both can lead to a nasty condition called latchup. This is what I call the current death-spiral where the effected circuitry starts to cycle and feedback ever larger currents, staying locked into this condition, and the only way to stop it is for something to burn out or the chip to be turned off.
Chip designers make allowances for backdrive and put in protection for this (resistors), but they only protect so far...so, if you undervolt enough, well...
So, this can happen on the IO pads of the chip, but really can happen anywhere you have voltage level shifters in the chip. Think about it--you have I/O signals coming into the chip at, say, 3.3 V (maybe 2.5 V) while the chip core runs at 1.3 or 1.1 V. In order for input signals, say, from the video memory, to get into the core, they have to be voltage-level shifted down to what the internal circuitry needs. It's at these voltage shifters were backdrive and thus latchup can most likely occur--remember, you usually don't have control of the I/O signal voltage (say, from the ICH northbridge or from a Video RAM, or whatever) and yet you're lowering the voltage to the transistors that have to handle this voltage.
Oh, I almost forgot: luckily, usually the chip stops working before backdrive/latchup occurs because of various reasons, thus protecting you from seeing the magic gray smoke coming out of the chip.
Too much undervolting can cause something called latchup. This is bad. Avoid.
DISCLAIMER: I am a chip designer working for a company that designs multi-voltage chips for servers, notebook PCs, and desktop PCs.