Considering nobody has responded, I'm wondering if the question was phrased poorly, placed in the wrong forum, or simply not interesting. But for what it's worth, I did find a way to cause a SQL Server shutdown on a trace with the shutdown_on_error property.

First I created a server-side trace file (call it mytrace.trc) with option 6 (rollover 2 + shutdown_on_error 4). I set the maxfile size = 1 MB. Then I added the SP:statement event to the trace and started it. Afterwards, I created a text file in the same directory called mytrace_1.trc. Finally I began running sql queries until the trace file filled up to 1MB. Once it hit that point, it tried to "rollover" and create the next file in the trace sequence (mytrace_1.trc) but couldn't since it already existed. At that point, SQL Server stopped. I don't think this was something that would happen in real life but still it was kind of interesting.

After working with server-side traces and C2 auditing, I think the shutdown_on_error property exists simply so you can create audit traces that behave in the same way as C2 auditing but without all the overhead.