Ok, the envelope game. You can rework it to say the second envelope contains the next vulnerability in the queue of vulnerabilities. An empty queue is just as valid as a non-empty one, so if there are no further flaws then the envelope is empty. That way, all states are handled identically. What you REALLY want to do though is add a third envelope, also next item inquire, from QA. You do NOT know which envelope contains the most valuable prize but unless two bugs are found simultaneously (in which case you have bigger problems than game theory), you absolutely know two of the envelopes contain nothing remotely as valuable as the third. If no bugs are known at the time, or no more exist - essentially the same thing as you can't prove completeness and correctness at the same time, then the thousand dollars is the valuable one.
Monty Hall knows what is in two of the envelopes, but not what is in the third. Assuming simultaneous bug finds can be ignored, he can guess. Whichever envelope you choose, he will pick the least valuable envelope and show you that it is empty. Should you stick with your original choice or switch envelopes?
Clearly, this outcome will differ from the scenario in the original field manual. Unless you understand why it is different in outcome, you cannot evaluate a bounty program.
Now, onto the example of the car automotive software. Let us say that locating bugs is in constant time for the same effort. Sending the software architect on a one-way trip to Siberia is definitely step one. Proper encapsulation and modularization is utterly fundamental. Constant time means the First Law of Coding has been broken, a worse misdeed than breaking the First Law of Time and the First Law of Robotics on a first date. You simply can't produce enough similar bugs any other way.
It also means the architect broke the Second Law of Coding - ringfence vulnerable code and validate all inputs to it. By specifically isolating dangerous code in this way, a method widely used, you make misbehaviour essentially impossible. The dodgy code may be there but it can't get data outside the range for which it is safe.
Finally, it means the programmers failed to read the CERT Secure Coding guidelines, failed to test (unit and integrated!) correctly, likely didn't bother with static checkers, failed to enable compiler warning flags and basically failed to think. Thoughtlessness qualifies them for the Pitcairn Islands. One way.
With the Pitcairns now overrun by unemployed automotive software engineers, society there will collapse and Thunderdome v1.0a will be built! With a patchset to be released, fixing bugs in harnesses and weapons, in coming months.