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What releases the magic blue smoke when you exceed working voltages or reverse the supply voltage?

Applied to any 'chip'

Excessive current producing excessive power dissipation (\$I^2 R\$) and/or excess voltage causing insulation breakdown due to high internal field strengths coupled with the lack of thermal conduction from the devices inside the chip.

Consider the non-linear, asymmetric (polarity sensitive), physically small nature of the internal devices and their small heat conduction paths. Couple this with low voltage destruction of very fine insulating layers (high field V/m) producing bi-directional low resistance conduction pathways.

The internal individual device temperature rises very quickly and destroys its semiconductor/insulating properties. Once destroyed this produces other low resistance pathways causing multiple cascading failures across other devices on the chip.

All this happens very quickly and its very much a one way event. (Think Humpty Dumpty - Putting all the pieces back together won't get you back to where you started from - Humpty has left the building)

How could you repair it?

Basically you can't cause magic doesn't exist. There would be so many interacting faults in the circuit that it would be nigh impossible to localize any fault. (Remember even in a 'simple' IC you are dealing with hundreds of thousands of devices.) All faulty devices would have to be identified and replaced at the same time (assuming you had the ability to reconstruct all faulty devices at an atomic level) - miss only one and you have to start again when you power up.

Simple solution (and most cost effective in time and money) throw the dead bug away,learn by the experience, replace it with a brand new full spec chip and next time be more careful with the power supply.