What happens if account goes to zero BEFORE expiration? Do they close it automatically? I know accounts will close at expiration if no action is taken prior to expiration
I have lot of those zero value long calls, more after today. They all stay open until expiry. Most, I couldn't even give away.
If the options aren't expired they're not worth zero. I'm guessing you're talking about options that are zero bid at five cents. Although those are technically so far out of the money they will unlikely never be in the money, but it does happen, and the zero bids have a small chance to have value. I imagine last week there were plenty of puts that had zero bid that are now in the money. But to answer your question they won't disappear until they expire.
There is no zero bid at zero, any market maker will be happy to sell you something that's worthless for nickel.