There's a bug. readline() should be read_line(). You'll need a timeout also. This works:

#!/usr/bin/perl

use strict;
use warnings;
use Net::SSH::Expect;

my $ssh = Net::SSH::Expect->new(
    host     => 'localhost',
    user     => 'user',
    password => 'password',
    timeout  => 1,
);

warn "Starting SSH...";
$ssh->run_ssh();

warn "Testing login output...";
my $login_output = $ssh->login();
print " Done", "\n";

my $who = $ssh->send('ls');
my $line;
while ( defined ($line = $ssh->read_line()) ) {
    print $line . "\n";
}
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