Here's what's going on from the limited description of your problem and your setup:
What I understand:
You have the Greddy Type-S installed replacing the stock BPV. You have the vacuum lines set up just like stock and the tubing set up just like stock as well. When you take the tube off of the Greddy Type-S it sounds nice, but the car idles rough and stalls. When the pipe is in place it does not sound at all, but the car runs fine.
If any of this is wrong, please correct me.
What the problem is:
There is no problem. You installed the Greddy Type-S as a recirculating BPV (bypass valve). The reason why you aren't hearing anything is the same reason why you don't hear the stock valve recirculating. The stock intake piping muffles all of the sound. When you take the tube off you turn the Greddy Type-S into a blow off valve, venting to the atmosphere. The reason why your car dies with this set up is because the air you are venting is metered, so the engine expects it to get there. When it doesn't you A/F goes very rich, flooding your engine.
Solution:
Don't do anything, because nothing is broken. Hearing a BOV doesn't mean it's not working. It's working better than the stock in most cases. If you want to hear it, replace the stock intake. In most cases your going to get turkey.