Yes you can get updates sent to your handset. Please go to the following link to learn about Facebook commands: https://www.facebook.com/mobile/texts.php
Example: subscribe George
To turn it off you can send “unsubscribe username” to 2266
Note: using subscribe/unsubscribe username from your phone only stops notifications to the place the command comes from; you'll still able to collect a person's updates on the web.
Or they can visit the website and switch the alert for mobile devices on/ off.