Closed is right. This is different from showing 0 (zero), because the 0 may easily change into 1, 2 or even 9 within hours.

But don't take a "C" from one site as gospel. I've just booked an N class seat (lowest fare sale class) on a BA longhaul. Yesterday I was getting C's or 0's from different sites in different countries, and was looking at a V fare instead. Waiting until today, I got an N seat which had come back into the system, when the German site continued to insist on "NC".