You can use the .close() method to instruct the serial port to close:

myserialport.close(function (err) {
    console.log('port closed', err);
});

.on('close') allows you to add the function as a listener of the 'close' event. But, it will simply wait for the event to occur (to be emitted) rather than instruct it to be done.

As you can see in /node_modules/serialport/lib/serialport.js: close-event may not be emitted (unlike disconnect).

You can add console.log locally like below to simple debug.

P.S. I tested it on Win7x32. Close-event is emitted.

SerialPort.prototype._disconnected = function(err) {
  this.paused = true;
  this.emit('disconnect', err);

  // add: console.log('1', this.closing);

  if (this.closing) {
    return;
  }

  // add: console.log('2', this.fd);

  if (this.fd === null) {
    return;
  }

  this.closing = true;
  if (process.platform !== 'win32') {
    this.readable = false;
    this.serialPoller.close();
  }

  // add: console.log('3');

  SerialPortBinding.close(this.fd, function(err) {
    // add: console.log('4', this._events.close.toString());

    this.closing = false;
    if (err) {
      debug('Disconnect close completed with error: ', err);
    }
    this.fd = null;
    this.emit('close'); // it's your target
  }.bind(this));
};

Reconnect example

var SerialPort = require('serialport');
var port = new SerialPort('COM1', {autoOpen: false, baudRate: 9600});

function open () {
    port.open(functon (err) {
        if (!err)
           return;

        console.log('Port is not open: ' + err.message);
        setTimeout(open, 10000); // next attempt to open after 10s
    });
}

port.on('open', function() {
    function send() {
        if (!port.isOpen()) // v5.x require
            return console.log('Port closed. Data is not sent.');

        port.write(123, function (err) {
            if (err)
                console.log('Error on write: ' +  err.message)

            port.drain(() => console.log('DONE'));
        });
    }

    setInterval(send, 1000);
});

port.on('close', function () {
    console.log('CLOSE');
    open(); // reopen 
});

port.on('data', (data) => console.log('Data: ' + data));
port.on('error', (err) => console.error('Error: ', err.message));

open(); // open manually

If you really only want to read one line (like posted in your comments) try to modify your code like this:

// make connection using readline as provided in your example

var line = null;

serialPort.open(function () {
  console.log('open');

  serialPort.on('data', function(data) {
    console.log('data received: ' + data);

    if (data.trim() !== '') {
      line = data;

      serialPort.close(function () {
        console.log('closing');
      });
    }
  });
});

// now you may work with your "one" line:
console.log('line strored: ' + line);

This only fetches the first non-empty line received of course.