I have a 12-in Mansfield 4000 series outdoor frost-free faucet (according to this). It's leaking from inside the stem tube (labeled "1") only when water is turned on. Removing the stem from the faucet, I cannot see light from the stem tube end. However, when I carefully dripped water into the stem tube, a little of that water came out from the holes labeled "2". This makes me suspect that there might be a hole (I assume I have to replace the entire stem in this case) or a deteriorated washer inside the stem. Is Prier a new owner of the Mansfield brand? According to them, the stem should never leak this way.
It turns out that an o-ring (400/500 Stem End O-Ring in the diagram below) is completely absent. Since there is no leak when water is turned off, the washers should have been fine. When water is turned on, the stem end will be pushed against the thick copper part, thus closing the holes. With the o-ring missing, water drips through the seam, into the holes, and out from the handle thread.
That is a standard washer based faucet. Turn the water off pull the packing temove the shaft at the end there will be a small rubber washer that needs to be replaced. The washers when new are volcano shaped round with a hole and taller in the center. Remove the screw and old flattened washer, put the shaft back in and screw it in then put a few wraps of valve stem packing on the shaft and replace and tighten the nut , turn the water on this will keep it from dripping when turned off or on with a hose on it and is a complete rebuild.