That hose is breather. You can leave it hanging. It could spill some oil occasionally. It doesnt have any effect on engine when disconnected from intake. Dont know why your car is "dying", I was driving my car without any (I didnt had anything before throtlle plate) air intake for about 2 months. Breather hose was hanging and IAT sensor was hanging too.
By the way.. Where you put you incoming air temperature sensor?
You can get breather filter from ebay and put it on the end of that hose you were talking about. Or on the valve cover, where that hose is connected. Remove the hose and put a filter.