from someone who has been there a few times..yes they can suspend your license without you knowing about it. however, when that happens, there is usually a note put on your DMV record thats states 'not notified' so if you get pulled over the officer can't charge you with driving on a suspended license. as for the suspension for not updating your address...check with an attorney (free consultations are good) and see what he/she can tell you. seems a little harsh to me...it could just be as simple as letting them know the new addy and paying a small reinstatement fee...
