I just went through this as there was an issue with my CC and not being able to resub. So, for an entire week I had to call ZOS customer service each nigth to get a day added to my account until they sorted this issue out. So, every night for more than a week, my game time was expiring at 7PM my time.
Basically, you can keep playing on the current session that you are on. But, if anything happens that requires your account being polled, like logging out, you will be not allowed to log back in.
I think one time I was actually kicked from the game, but that could have been some server hiccup that caused this. Or it could have been some other mechanism that noticed my account expired. No, you can't just pause the game either while logged in, as after 10 minutes or so of inactivity, you are kicked from the game.
So, you can play for a little while if your sub expires during the session, but not for very long.
Enjoy the game, life is what you really want to be worried about.
PakKat "Everything was going well, until I died"
Gary Gravestink "I am glad you died, I needed the help"