It is called an air reserve. Same concept as in the gasoline tank of a motorbike, the valve has three positions, close, open and reserve. In open position, a couple of liters of gasoline remain trapped in the tank, and can be used only turning the lever to "reserve".
It is exactly as a pony bottle (but with less safety, as already discussed). It is air you carry with you and it is a reserve in case you finish the main tank.
Conceptually it is like having a smaller main cylinder and a pony. Unfortunately, it appears that American J-valves had a bad tendency to be opened by error, vanishing the safety of such a reserve.
Italian J-valves could not be opened by error before the time, and always carried a double regulator post, so they were close the safety of a true pony (if fitted with a double regulator, as it was standard practice here).
It must also be said that in Italy no one was diving a single cylinder. The Aralu tank I posted earlier was a twin set, and the reserve was acting on just ONE of the cylinders, and tuned to 100 bar. Below that pressure, the cylinders are separated, and you breath only from the left one. When it is empty (and the pressure reduces progressively, giving you ample time for reacting) you pull the rod, the reserve opens, and the 100 bar on the right cylinder partially travel to the left one, making a typical sound "tweeeinng"....
The right cylinder becomes cold, and the left cylinder becomes hot (you feel this if diving naked, as it was common in summer here in Italy).
If you had a SPG, you will find the pressure raising from almost 0 bar to 50 bar when opening the reserve.
I did never consider the reserve fully safe on a single cylinder, without also having an SPG.
It was fully safe only on a twin cylinder with the Technisub valve, which in facts was the standard at the time.