I'm curious to know if it's possible for a CPU to get fried/damaged in such a way that it still works, but you get glitches or BSODs.
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Definitely possible...a mechanism called
electromigration that occurs constantly any time a device is powered on. All semiconductors are subject to it.
When a CPU is degraded with electromigration it will no longer be stable at an operating clock and voltage it used to be stable at. It seems to operate OK but you'll get random application crashes to desktop, BSOD's or even outright restarts that you never used to get. When just starting they're frequently spaced out in time and that makes sense as it may need the combined stress of a high boost clock, voltage, and temperature on the particular degraded processor circuit to show itself.
Electromigration is accelerated when operated at high(er) junction temperature and current. So we tend to see that with heavily overclocked systems that are run a long time in heavy processing. It's easy to see why GPU's suffer more from it, so you see it more often, as they operate super hot even stock. They also have a lot of overclocking headroom stability to exploit. But it only lasts so long till it starts going unstable and the overclock is backed off.
CPU's are a little less frequent to see, probably because most people who overclock them don't run all cores under max processing loads for hours on end like GPU's are when gaming. And those who DO have need to run a CPU that heavily know the dangers of overclocking and do it reasonably, if they do it at all.