What is this? HELP!!!!

So I tried cleaning the IAC, MAF, changing the VSS, but I've discovered that when I touch the hose to the right of the IAC in the picture the car stalls. It seems to be either glued or melted on is this normal? what is this part (its like an air hose) and can this effect the idle as well? The motor still idles irradic. http://lib.store.yahoo.net/lib/mustangtuning/crides000033-2.jpg

Only rough at Idle? Also, when did it start having a rough idle? Checked all plugs, wires, coil pack, etc? Not doubting you, just covering the bases. I don't see why it would stall when you touch the hose..