$fh is a file handler, i.e. it is actually an iterator on a file, so that each time you read from $fh, you get the next line. In your sub, your my $fh = shift; actually creates a new copy of $fh each time the sub is called. It still works because $fh "knows" which is the next line to read from the file. But your anonymous sub is not a closure; the alternative code I wrote is actually keeping its own copy of $fh, my anonymous sub actually closes on $fh. Please note that an anonymous function is not necessarily a closure, and a closure does not necessarily have to be anonymous (although is is often the case).
You might want to have a look to this: Closure on Closures.
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