When I had my own apartment in Zurich back in 2000, I did not pay any billag taxes as I did not approach the government to advise them of my use of television/radio. I believe if you don't register with the billag, there will be a billag man knocking on your door one day checking to see if you have a television/radio. And since I had moved out after 12 months, the billag never showed up.
A similar situation happened to a friend of mine who did not register either. In his case, my friend then lied to the billag guy saying he has just moved a few months ago instead of admitting he lived there for 2 years.
Also, my ex girlfriend does not pay either (more than 1 year now). Her strategy is she would never open the door to anyone she does not know ;-)

I guess because of data privacy the billag does not know when some is moving in. I'm not sure though...
eric