First of all, the file open does not need to go into an eval. Secondly, as far as I can see the else will trigger on a successful run (ie no error)
Are you sure the uunwritable file is really unwritable? and that you arent just successfully opening the file?
UPDATE: Looking at the examples in the docs for Exception::Class they seem to make the assumption that your eval always throws an exception. Try changing

ref $e ? $e->rethrow : die $e;
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to

ref $e ? $e->rethrow : die $e if $e;
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It says that caught without args simply returns $@ (which if successful will be undef), so that will keep it from throwing the empty die you are seeing