I actually simulated this situation, of loosing the regulator's air after a first stage failure just after an exhale. I was in a pool that was 16 feet deep, but made an emergency swimming ascent that covered 25 yards of the pool (simulating an ascent from 75 feet depth). Not only was I able to accomplish it, I was able to blow bubbles for the last part as I ascended from 16 feet.
You see, there is always Air still in your lungs even after an exhalation. We have what is called out "tidal volume" in our lungs, which is the amount of air we normally inhale, and exhale when breathing. There is also what is called our "expiratory reserve," which is the amount of air which we normally don't exhale during our breathing cycle, but that we can still force out. Below that, we also have our residual volume, which is the amount of air still in the lungs which we cannot exhale, but is still there. Between the expiratiry reserve, and the residual volume, there is about a 2 liters of air still in our lungs. This is enough to swim 75 feet without too much problem (at least for me).
Now, let's do a mental exercise; if you are at ~100 feet depth (say 10 meters), and have this regulator malfunction where you cannot get air after a normal exhalation, and start with 1 liter of air in your lungs, how much air will you have if you do a slow emergency swimming ascent to the surface? Well, we know that we are at 4 atmospheres absolute pressure. As we ascend, that air expands due to lessening of the pressure. Because the air is 4 times as dense at 30 meters (4 ATM absolute), we can expect that air to expand by four times. So, heading to the surface, starting with only two liters of air in our lungs, that will translate to eight liters of air by the time we reach the surface. Most people have a vital capacity of only 4-5 liters of air, which means that in the CESA, we'd have to blow out some 3-4 liters of air to avoid lung over-expansion. Jacques Cousteau, in his book The Silent World, described Frédérick Dumas teaching some of the first scuba courses in the 1950s, and requiring for graduation that the students complete a CESA from 100 feet to give the students the confidence that it can be easily accomplished. This assumes a no-decompression dive, but this was done for a number of years.
When I went through the U.S. Naval School for Underwater Swimmers in 1967, we were required to complete a buoyant ascent, using the "blow and go" technique (blow out all the air from your lungs, then let go with an inflated life vest, and go to the surface from 33 feet. We were to continuously exhale throughout this buoyant ascent too, showing that there was still air in our lungs after the "blow" portion.
SeaRat