That's one of the things an auto shop can do for you. You don't need a new serial number or database; your VIN is good enough. But of course a thief can grind that off.

The other one is welding on the converter. It doesn't make it unstealable; but it's just not a quickie extraction anymore.

If your question is (as it should be), "What about legitimately fixing the converter? Can you still do that?" , I don't know.