Final answer:
Without the main method or its contents, it's impossible to determine which exception the provided Java program code may throw. The provided code snippet does not have sufficient information to ascertain an exception.
Step-by-step explanation:
The question asks which exception will be thrown when a specific Java program is run. However, based on the given code snippet, it is not possible to determine the exception since the main method and its contents, where an exception could occur, are not provided. The code piece shown only declares a class implementing AutoCloseable with an uninitialized string variable header, but does not contain any operations that would throw an exception. Therefore, without additional code, we cannot confidently say which exception, if any, will be thrown. However, the options provided suggest that it is asking about runtime exceptions, and among these, IOException and ClassNotFoundException pertain to exceptions that could occur during file handling or class loading respectively, CompileError is not a standard Java exception but would indicate a compilation failure, and 'No exception will be thrown' suggests that the code would run without errors. If the main method is absent or has no exception-triggering code, then no exception would be thrown.