> The power supply shall contain protection circuitry such that the application of an input voltage below the minimum specified in Section 3.1, Table 1, shall not cause damage to the power supply.

From section 3.1.3 of Intel's ATX12V power supply design guide - http://www.formfactors.org/developer/specs/ATX12V_PSDG_2_2_public_br2.pdf

Power supplies have an input section composed of a bunch of silly circuitry that, at the end of the day, provides about 308 VAC to a transformer, which then powers the regulation and conditioning circuitry.  This silly circuitry actually forms the major basis of the regulation circuitry, and if you are using less than the full wattage of the power supply may be able to manage with significant undervoltage conditions without falling out of regulation on the output side.

When a brownout occurs, the powersupply will attempt to deliver the rated current for as long as it can (based on the incoming voltage and current) and if it cannot maintain regulation it'll deassert the `Power Good` signal going to the motherboard.  The motherboard is responsible for deasserting the `power on` signal going to the supply, and if it does so in time, then the supply will drop all it rails and turn off.

If the motherboard fails to do this, the powersupply should drop its rails when it falls too far out of regulation, but that is not guaranteed, and with low quality power supplies you may find your components and motherboard receiving undervoltage conditions as well.

What happens at that point depends on how robust those components are, but it's generally not a good thing.