When I bought my Expedition in the fall of 1999, the dealership didnt do the registration paperwork properly...I think the registration date was all zeroes or something stupid like that.
So while I was issued a set of plates, the DMV never sent me a renewal notice and I was so busy I never thought of it. Until sometime in 2003 when a friend said "hey, you know your license plates expired two years ago?"
I guess it depends on how observant the local police are. When I first moved to CA from MA and had been here for about 3 weeks I got pulled over by a CHP who told me he'd seen my MA plates several times and that I needed to register the car in CA if I was going to be here for more than a few more days. He was probably BSing me about having seen the plates before and remembering it, but...
I did however go on to drive with the MA plates for almost a year without ever getting stopped again, until they expired.
MA did go through the trouble of finding me so they could send me an excise tax bill. I sent it back to them with "No thanks, losers" written on it.