They do actually (once upon a time I was an avid overclocker) but that's only when you seriously overclock and overvoltage the chips and in this case, the inadequate cooling system speeds up the process so the degredation*** process takes effect and after that, it's just a matter of time. This is not the OP's or AF3's case though, not even close.
A blown up chip is also kinda rare nowadays since most if not all chips have internal thermal/power protection (first they will start to throttle down and in extreme cases they will shut down to protect themselves). The first and last time I blew up a chip was like 20 years ago and it was an AMD Athlon, those didn't have a built in thermal protection system (the thermal sensor was on the motherboard not inside the CPU) so once the cooler totally failed (and of course the motherboard sensor had failed as well, thanks Murphy!), it gave up the ghost (with a nice puff of smoke) a couple of minutes later.
***When a chip starts degrading it just can't normally operate at the nominal frequency and voltage without errors, so when that happens the only options are to either drop the frequency, or pump up the voltage or both these.