Welch plug popped out

Either the plug was not installed correctly or there was an issue with it being the correct size. Did the engine overheat? How long was it run hot? If a short time you might be able to put on a different head and gasket and revive it. I would probably do a compression test and a leak down test, just to see what you still have.

Well if the coolant got low and turned to steam and the head got hot, that may have made it fail. Really hard to tell which way it went though. I would still test it, I have seen a few engines surprise me after I was sure they were fried.

There are a few types of plugs used on engines. There are the Core plugs these look like a cup with straight edges. Then there are Welch plugs, these are simple domed round parts, then there are threaded pipe plugs. Those are the ones in the images attached. In the last picture you see an engine kit for a GM, it uses all three types, as do most engines made these days.
I have seen radiators with plugs in them but not often. If they use one of those styles of plug it could come out under pressure to prevent other damage. Because this is a diesel the compression pressure is much higher. If the head gasket was compromised that pressure could easily push out a core plug or break a radiator. However a bad radiator could have leaked enough to cause an overheat which could also do the same. Determining which way things went would require a full inspection and even then it would be a toss up if it was correct.

That should have been a cup style. From the appearance of the bore that can be seen it looks like the plug that was used was a bit undersized. Also looks like they used a bit of sealer, which is not uncommon but really should not be needed if it is the correct plug. Another possibility was that the plug was not installed straight into the hole. If they are installed at an angle they will not seal properly and can fail.
You did not find the plug by chance? It would show far more.
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That is the hard part. Sort of like the circular argument over the chicken or the egg. If it is a metal radiator core you might find corrosion or damage near the holes, that could show the radiator was failing. However, it does not really say which failed first. One thing that could show which it was would be how it overheated. If it was running at normal temperature and then you had a sudden spike, lots of steam and a large puddle it would point more toward the core plug as it would dump coolant very fast. Probably your best bet would be the have the shop look it over and see which they say caused the failure as they can actually see it all in person.

Sorry, I cannot give you a definite answer. I take it the company/person who did the re-man work is balking at replacement? Good luck. I hope they either stand behind their product or at the very least offer to pay the labor to repair the issue.
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