When the monsters start showing up as 0/0 untargetable masses and I end up having more of a card in play than I had in my deck to begin with, we are no longer playing Elements. We are playing some sort of bizarre guessing game based on Elements. There has to be some way for the server to recognize that impossible things are happening - at least have either side report when it sees a 0/0. When it sees something like this, the game shouldn't just continue and ignore it. It's frustrating, and you're punished for quitting.
So short of actually fixing the sync problem, I'd say there are two reasonable options. First, just end the match in a draw. It sucks, but it's better than playing through that insanity. Second, split the match into two and have each player continue separately vs. an AI.
At least a quarter of the PVPs I did today included something ridiculous happening. Yeah, I checked, there's nothing wrong with my net connection. This game is a lot of fun, but it really needs to behave itself.