Not true, at least not in my experience. I’ve actually had CPU cores turn off, or underclock, after various system malfunctions.
Example 1: was overclocking an AMD X2 6400+, during stress testing the system shutdown. At next boot, I only had 1 processor available (i.e. view the Performance tab in Task Manager, and Device Manager only reported 1 CPU). After I reseated the CPU (could have been removing power from the motherboard, looking at it retrospectively) both cores were available again.
Example 2: friend asked me to take a look at their system to resolve a BSOD issue. While poking around in the BIOS (on a system with a stock-clocked CPU) the power went out, and when I resumed testing, the CPU had underclocked (but no other settings had changed, nor had defaults loaded).
Can’t explain it, but I’ve seen it 
