The obvious thing to check is your CPU temperatures. Unlocking an extra core increases the heat produced by the CPU. If you're using a CPU cooler which was designed for the original CPU's TDP, then it may not be able to pump heat away fast enough from the unlocked CPU. And your problems would then be due to the CPU overheating.
If the temps are fine, then the prognosis isn't good. Extra cores aren't always locked just to create a new CPU for a lower marketing segment. Sometimes they're locked because the core was defective when tested. It's possible the extra core has a defect in a function which is only used by games.
Have you tried running a stress test on it? Ideally you want something that will test every function available on the CPU. I'm not sure if Prime95 does that, but since it's used to test overclocking that's probably a good place to start. There's a stress test from Intel which tests all the functions on Intel CPUs, but I don't know if it's applicable to AMD CPUs. (Be sure to monitor the temps while stress testing too.)
Alternatively, you could try limiting the processor affinity for the game (task manager -> details -> right-click) to just the original 2 or 3 CPUs and see if that makes the crashing problem disappear. If the crashes happen only when the game is allowed to use one particular core, then you've most likely got a defective core. If that's the case, you *might* be able to get it working again by bumping up the CPU's voltage. But that will generate more heat which could cause problems with the other cores.