... assuming that the prices never goes up and bitcoin ceases to exist or looses value completely, will this forum continue to function?
Yes, in that case it would cease to exist, just as if a meteorite fell and caused the extinction of the human species, as happened with the dinosaurs. The question is how likely it is that this would happen.
Price drops like the recent one and bear markets do not end the forum, as other colleagues have already told you. If anything, activity is reduced.
Have seen threads like this in prior dumps too, this forum did fine when Bitcoin was close to worthless, it will do just fine.
It is logical. And in bull markets are more typical threads along the lines of "Will Bitcoin price reach $1M next week?"
I'm exaggerating, but I think you get the idea.