That's how sed behaves, too, and many other tools.

If you want to handle missing files, don't use the diamond, use open or something like

BEGIN { -f or die "No file $_" for @ARGV }
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BTW, $! only contains a meaningful value right after something went wrong. If you print it after processing an existing file, its value might be totally irrelevant (I'm getting Inappropriate ioctl for device).