Graphite packing rope squeezes out between valve stem and packing nut
Using the graphite rope isn't as easy as you would think. First off, you need the right size rope that fits in tight with one wrap. You don't use a continuous piece. You cut a piece equal to the circumference and push the rope in and butt joint the ends. Then do it again with another piece of rope and rotate it so the ends don't even up with the previous layer ends of the rope. Keep doing this until the nut is full.
Better yet, get one of these kits. Picture from Granger.com