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termination.patch, in the result handler you've added:
 while cache and thread._state != TERMINATE and not failed
why are you terminating the second pass after finding a failed process?
Unpickleable errors and other errors occurring in the worker body are not exceptional cases, at least not now that the pool is supervised by _handle_workers. I think the result should be set also in this case, so the user can inspect the exception after the fact.
I have some other suggestions too, so I will review this patch tomorrow.
For shutdown.patch, I thought this only happened in the worker handler, but you've enabled this for the result handler too? I don't care about the worker handler, but with the result handler I'm worried that I don't know what ignoring these exceptions actually means. For example, is there a possibility that we may lose results at shutdown?