Yes, there is potential for a semi-broken CPU to function.
Yes, there is potential for a semi-broken CPU to function.
I've dealt with random restarts on my i7-8700 when running demanding tasks. By disabling the last core in Task Manager, the issue disappeared. For upgrading to an unRaid server, I'm considering CPU pinning and isolation. However, even with isolation, cores can still fail sometimes. Recent attempts to adjust vcore settings or run OCCT without problems haven't resolved the problem. It seems risky to rely on this setup for a server. You might want to explore other CPUs or consider alternatives if stability remains an issue.
What type of power supply are you using? Such immediate shutdowns are often signs of a faulty PSU or overheating shutdowns.
See if boosting CPU voltages is possible. Raising the Vcore could be beneficial.
I don't think there is any way of fixing your situation other than isolating the core. That said, I don't use Unraid, so I have no idea how to give its bootloader any kernel-parameters, but passing e.g. "isolcpus=5,11" to the kernel would isolate the core and its hyper-threaded, virtual core from the rest of the system. See e.g. https://www.linuxtopia.org/online_books/.../re46.html