First, let's try non-SSL, here's the client:

#!/usr/bin/env perl

use strict;
use warnings;

use IO::Socket::INET;

# create a connecting socket
my $peerhost = 'localhost';
my $peerport = 8000;

my $socket = new IO::Socket::INET (
        PeerHost => $peerhost,
        PeerPort => $peerport,
        Proto => 'tcp',
);

binmode($socket, ':bytes');
$socket->blocking(0);

for(my $i = 0; $i < 5; $i++) {
    syswrite($socket, chr($i));
    sleep(2);
}
[download]

And the server:

#!/usr/bin/env perl

use strict;
use warnings;

package TestServer;

use base qw(Net::Server);

sub process_request {
    my ($self) = @_;

    binmode(STDIN, ':bytes');
    STDIN->blocking(0);

    while(1) {
        my $buf;
        sysread(STDIN, $buf, 1);
        if(defined($buf) && length($buf)) {
            my $num = ord($buf);
            print STDERR "GOT $num\n";
            last if($num == 4);
        } else {
            print STDERR "...doing something else...\n";
            sleep(1);
        }
    }

    print STDERR "Done.\n";
}

TestServer->run(port => 8000);
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As expected, the server runs the "doing something else" part when there's no data arriving from the client:

2015/04/09-10:58:23 TestServer (type Net::Server) starting! pid(7799)
Resolved [*]:8000 to [::]:8000, IPv6
Not including resolved host [0.0.0.0] IPv4 because it will be handled 
+by [::] IPv6
Binding to TCP port 8000 on host :: with IPv6
Group Not Defined.  Defaulting to EGID '1000 4 20 24 27 30 46 108 124 
+125 130 1000'
User Not Defined.  Defaulting to EUID '1000'
GOT 0
...doing something else...
...doing something else...
GOT 1
...doing something else...
...doing something else...
GOT 2
...doing something else...
...doing something else...
GOT 3
...doing something else...
...doing something else...
GOT 4
Done.
[download]

So far, so good. So, let's change this to SSL. First, we need a self signed certificate:

yes '' | openssl req -x509 -newkey rsa:2048 -keyout key.pem -out cert.
+pem -days 10 -nodes
[download]

Next, we modify the client to use IO::Socket::SSL instead of IO::Socket::INET:

#!/usr/bin/env perl

use strict;
use warnings;

use IO::Socket::SSL;

# create a connecting socket
my $peerhost = 'localhost';
my $peerport = 8000;

my $socket = new IO::Socket::SSL (
    PeerHost => $peerhost,
    PeerPort => $peerport,
    Proto => 'tcp',
    SSL_verify_mode => SSL_VERIFY_NONE,
);    

binmode($socket, ':bytes');
$socket->blocking(0);

for(my $i = 0; $i < 5; $i++) {
    syswrite($socket, chr($i));
    sleep(2);
}
[download]

Then we configure Net::Server to use SSL and our self-signed certs:

#!/usr/bin/env perl

use strict;
use warnings;

package TestServer;

use base qw(Net::Server);

sub process_request {
    my ($self) = @_;

    binmode(STDIN, ':bytes');
    STDIN->blocking(0);

    while(1) {
        my $buf;
        sysread(STDIN, $buf, 1);
        if(defined($buf) && length($buf)) {
            my $num = ord($buf);
            print STDERR "GOT $num\n";
            last if($num == 4);
        } else {
            print STDERR "...doing something else...\n";
            sleep(1);
        }
    }

    print STDERR "Done.\n";
}

TestServer->run(port => 8000,
                proto => 'ssl',
                SSL_key_file => 'key.pem',
                SSL_cert_file => 'cert.pem');
[download]

Here's the result of this run:

2015/04/09-11:04:03 TestServer (type Net::Server) starting! pid(8551)
Resolved [*]:8000 to [::]:8000, IPv6
Not including resolved host [0.0.0.0] IPv4 because it will be handled 
+by [::] IPv6
Binding to SSL port 8000 on host :: with IPv6
Group Not Defined.  Defaulting to EGID '1000 4 20 24 27 30 46 108 124 
+125 130 1000'
User Not Defined.  Defaulting to EUID '1000'
GOT 0
GOT 1
GOT 2
GOT 3
GOT 4
Done.
[download]

The server blocks on sysread() and does not run the "doing something else" part.