You are checking the wrong thing for defined().

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11141789
use warnings;

my $filename = 'tmp.11141789';

open my $fh, '>>', $filename or die "$! opening $filename";
printf "1) fileno = %s\n", $fh->fileno // 'undefined';
close $fh or die "$! closing $filename";
printf "2) fileno = %s\n", $fh->fileno // 'undefined';
close $fh or die "$! closing $filename";
printf "3) fileno = %s\n", $fh->fileno // 'undefined';
close $fh or die "$! closing $filename";
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Outputs:

1) fileno = 3
2) fileno = undefined
Bad file descriptor closing tmp.11141789 at ./pm11141789.pl line 12.
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This was run on ArchLinux, I don't have a Strawberry Perl system to test on.