What should I do when my CC opponent has closed his account?

It's a peculiar situation: Yesterday I accepted a challenge from the Correspondence lobby, 3 days per move. 1.e4 e6, the French defense.

Now I checked on my opponent's account, but he has closed it in the meantime, yet the clock is still running (on his side). Should I just wait until the counter reaches zero and then manually check on the game again, to confirm that his time is out, or simply "resign"? Would I lose points by doing so?

I've noticed in the past that games with 'ghost opponents' (people who close their accounts before the termination of a game) go on forever, if you don't click on them in the menu.

I assume you are talking about this game? lichess.org/S0NiH8PQ/black
I would just wait until the time runs out, if you resign you could potentially lose rating.

@Corridor Yup, that's the one.

It's just strikes me as weird, that fellow just created his account two days ago and now it's gone.

Well, sometimes people decide they don't want to play anymore I guess.

"I've noticed in the past that games with 'ghost opponents' (people who close their accounts before the termination of a game) go on forever, if you don't click on them in the menu."

This isn't related to people closing their accounts. It appears to me that anytime a correspondence game ends in a time out, the game just stays there in your active games until one of the players actually opens the game, then the result is confirmed. It definitely happens that way a lot, if it's not literally every single time.