Thanks for the suggestion. However, I wrote the spawned script and I know what exit codes it returns, and 13 isn't one of them. That's why I posted the question.
I discussed the situation with my boss, and he had me check the version of the Win32::Job Perl module on CPAN. The version number is 0.01, the script was written in 2002, and it's never been updated. So it wouldn't be surprising if the mysterious exit code value were the result of a bug. Therefore, I'm getting rid of the Perl module and writing my own code to do what I need.
Thanks for all the suggestions.