I replaced my fridge ice maker a few years ago because part of the circuitry burned out. The replacement has also now burned out (though not nearly as badly). For reference, the burned part is supposed to hold onto the end of a copper peg that leads to the heating element (which melts the ice slightly so it can be popped out of the mold).
It seems silly to spend $60 on a new one when it's just $0.05 worth of copper that needs replacing. Is there a safe way to fix this? Unfortunately, I can't just solder the connection because it is enclosed when assembled. For reference, those tabs aren't just fouled, they are burned completely through. My first thought is to pull out the whole trace, solder on new tabs (not sure where I'd get the material), and put the trace back in.
Above could be right though. If you can find a fridge ice maker that has lasted more than a few years without needing repairs, we all need to know. The failure here may be the 'safety' feature and continuous functionality may have been an at best minor concern.
I'm always wary of working on heating elements, don't over engineer it if you try to fix it and it could just be arcing like you suspect... but just remember that the wear/increased resistance on other items leading to that burned out contact may have contributed to that specific piece failing and you maybe should be thankful that it failed.
I have a 2003 Kenmoore fridge that came with the house that won't die. Ice maker works perfect. No repairs needed in the decade I've had it.