This first time your program tries to print to it, it can't, which creates another error, which it can't print, which creates another error, ...

So, closing STDERR will lead to an infinite loop if an error occurs. As is easily demonstrated:

 % perl
close STDERR;
die "ZOMG, infinite loop!";
__END__
 %
[download]

Or not. :)

Actually, writing to a closed file handle doesn't generate an error in most situations:

 % perl
close STDOUT;
print "Generate error!\n";
__END__
 %
[download]

If you enable warnings and use Perl code to write to a closed file handle, then you do generate a warning:

 % perl -w
close STDOUT;
print "Generate error!\n";
__END__
print() on closed filehandle STDOUT at - line 2.
 %
[download]

But the code that puts out that warning isn't Perl code and so doesn't generate a warning if the handle that it is writing to is closed. So not even the following causes an infinite loop:

 % perl -w
close STDOUT; close STDERR;
print "Generate error!\n";
__END__
 %
[download]

I can even go rather far trying to facilitate an infinite loop without causing one:

 % perl -w
my $loop; $SIG{__WARN__}= $loop= sub {
    $SIG{__WARN__}= $loop;
    print STDERR "Got: ", @_;
    print "Warn: ", @_;
};
close STDOUT;
print "Generate warning!\n";
die "Done.\n";
__END__
Got: print() on closed filehandle STDOUT at - line 7.
print() on closed filehandle STDOUT at - line 4.
Done.
 %
[download]

But, yes, close()ing STDERR is indeed a bad idea (for other reasons, which I covered in another reply).

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