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Techniques for dumping bit-rotten and/or damaged EPROMs:
Bit-rotten roms are EPROMs/EEPROMs/flash where the floating gate charges have decayed from age/light exposure below the threshold to reliably read as the 'high' state. On most EPROM based devices, a high floating gate charge indicates a 0 bit, so this means the values will read as 0xFF instead of the proper value.
There are several techniques to try to recover bit-rotten data like this:
Combining 2 or more of these techniques is significantly more effective than using them separately, so people have had much better luck both heating and simultaneously under-volting chips than doing either one separately.
Damaged Chips:
There are more or less two classes of damage to an IC which will prevent it from reading: Damage to the leadframe and bond wires, and damage to the die itself.
Heat might help for leadframe/bond wire damage (if it cannot be directly/permanently repaired with conductive epoxy or solder, etc) as it may make the metal expand enough to make contact with the other side it was broken off of.