sounds like the tube that just runs back into the lifter gallery. they just run into there. it just keeps the oil level at the rocker arms. There should be another small copper line that goes to the piece in the middle of the rocker arms as well this is the supply line. I am not sure which line you are talking about. one of them (with the narrowed end) just goes into the hole and what ever oil doesn't runout at the rocker arms gets poured down this hole. the small copper line comes from the other side of the engine through the block and up to that middle piece and supplies the oil to the rocker arms. If that is the one that is broken you need to get a new one, rocker arms need a little bit of oil....