I think roydm is onto the intent of what the customer requests. Durco calls it an "upstream relief hole" for their plug valves. If a liquid is trapped in the cavity and then vaporizes, the pressure can be enough to exceed the valve's rating (or worse). Drill a hole between the cavity and the upstream port, and the pressure in the cavity can never exceed the upstream pressure. Referenced low-emission packing would be appropriate for the liquid chlorine service that roydm mentions.
However, the vented plug will NOT help measure the leakage of the valve packing.
A vented BONNET, with lantern ring double packing, WILL let you measure the packing leakage rate, because any leakage that gets through the bottom packing rings will flow out the bonnet vent where it can be measured and directed to a safe reclamation point. The upper packing set will keep anything from making it to the environment.