open  OUT,'>'."$path/$name.faa" || die ("cannot open out $file $!\n");
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Unless joluito has been busy making uncited changes behind the scenes (update: /msg from pryrt says changes were made), the quoted statement is not present in the OPed code. However, I agree with your point about evaluation order in this statement.

... the real problem [is] setting the global variable $/

$/ = "\>";

and then never restoring it back to "\n".

Although trollishly delivered, I agree that failure to restore $/ is a problem, likely the root problem. No one else has made this point (update: yet — but see this).