I know it can't just be a random air hose, but the only hose that comes out of the airbox on the right (while facing the engine bay from the front) looks like it doesn't come from anywhere.
I recently switched my intake from the stock box to a Trust airinx, and i found it interesting, and a little unnerving, that this is the only hose that doesn't have an attachment on the new pipes.
then while trying to figure it out, i was looking at the airbox, and i noticed that it and the hose that it feeds on the other side of the airbox, are the only ones that don't pass through the air filter? they're sealed off.
So what does this hose do and where does it come from? the other hose that it goes to flows into the inlet manifold
I also noticed that the hose has no clamps on the bottom end, yet doesn't appear to be broken or cracked, so i don't think it broke off.
for refference it is part 13-571E on page 34
http://files.fdnewbie.com/1993_FD_Parts_Diagram.pdf

 

This is part of the relief system for the air pump----when the air pump is running anf provides more air than required,the releaf valve in the Air Control Valve opens and air is directed from the ACV to the rear of the air filter box--inside is a silencer and the mystery hose you describe vents the air coming through this silencer to atmosphere.It does not need fixing because the air flows out very gently.