The error handling options that are available in WinAutomation at Process level (i.e. sending an email with the error details, running another process or writing the error event to a text file) are only provided for Processes running via the WinAutomation Console.
A compiled Process (.exe file) is stand alone, which leaves no trail back except from the windows event logs as any other application would.
What can be done to handle unexpected errors, is to create an error handling logic with an Exception Block. Create an Exception Block and advice to run an error handling function in case any Action throws an error.
In that function, the last exception message can be captured, so as to write it in a text file on the desktop (or in any generic path you wish) or send it via email for instance.
This way for anything that happens within your process, you will be able to see what the error was and act accordingly or edit your process before compiling it again.
You can check a related Process by navigating to the following link: Global error handling in compiled Processes
You can create an .exe out of the attached .waj to see how it will perform.