A kill -9 wouldn't give you a chance to write the reason for termination to a file. It's the equivalent of the OS saying "you have already run your last CPU cycle, you will receive zero more CPU cycles, good bye".

You might be able to write the word "bad" in a file, and then clear the file if your app closes nicely. If you start and find the word "bad" in the file, then you know you were killed. A slight variation of what you suggested.