I'm not sure what your code is supposed to do. But if you want to check whether one list is a subset of the other, possibly with duplicates, I recommend using a hash of array references and "colliding" the elements out:

my %elements;

# open left file
while (<$left>) {
    chomp;
    # extract key
    my $key = $_;
    $elements{ $key } ||= [];
    push @{$elements{ $key }}, $_;
};

# open right file
while (<$right>) {
    chomp;
    # extract key
    my $key = $_;
    if (! exists $elements{ $key }) {
        print "Missing totally from left file: $_\n";
    } else {
        my $match = shift @{$elements{ $key }};
        print "Matched: $_ against $match\n";
        if (0 == @{$elements{ $key }}) {
            delete $elements{ $key };
        };
    };
};

for (keys %elements) {
    print "Only in left file: @{ $elements{ $_ }}"
};
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