I've over-simplified this a bit as it gets technical, but your question is technical, so let's dive in...
There are seven flight control computers (FCC) that take pilot input and translate that into flight control surface movement. They operate via a set of rules known as normal law. Normal law provides envelope protection, limiting speed, AOA, bank, pitch, yaw and G. Exceeding normal law limits can over stress the airframe. It's there to keep the airplane in one piece.
It usually works great. But if the FCCs lose an input from a sensor, as was the case in AF 447, then they can't accurately determine the envelope, and some of those protections are removed, allowing the pilot to fly beyond what would normally be allowed, since those limits might be inaccurately determined from faulty sensors. This regime is known as alternate and AF 447 was operating in alternate law.
The flight control system, in normal law, provides auto-trimming up to alpha prot (protection). You must hold back stick to fly an AOA above alpha prot. Release the stick and it returns to alpha prot. The airplane will be squawking at you the whole time you're at, or above in AOA, alpha prot by saying "speed, speed, speed" because you're at an unusually low speed. An unusually high AOA.
The airplane will limit AOA to alpha max. It can't be flown above that. It will stop increasing pitch.
Somewhere between alpha prot and alpha max, the flight control system engages alpha floor, and puts the engines in TOGA (full thrust). This is, as I mentioned, a safety limit to prevent a stall, and dig the airplane out of a low energy state.
Alpha floor and the speed warning are inhibited for landing (alpha max still applies, but the fuselage will hit the ground long before its reached) and this makes sense, you don't want a gust or momentary alpha sensor perturbation to suddenly put the engines in TOGA while landing - that would cause a crash all by itself. That inhibition happens at 100 feet (I was mistaken when I said 50).
Nothing in the FCOM (Airbus handbook for the airplane) or my airline flight manual states how much margin exists between these values. They're just a few knots apart, from alpha prot to alpha max, at normal landing speeds, and a good 20 knots below a normal landing speed. REALLY slow...but I've got no precise answer for you in either AOA or airspeed.
So, what really happened in this case?
First, the pilot flew well below the altitude that he should have. He, by doing that, removed the alpha floor and speed warnings.
Then, he continued to fly low, and didn't select TOGA power until the airplane was hitting trees. Usually, adding power before you crash works out better than adding power AS you crash...
Why?
He claims that "the airplane didn't respond" - which implies that he was expecting alpha floor to engage as he increased AOA. But it didn't because he was flying where it was inhibited for landing.
Had he selected TOGA before the end of the runway, the airplane would've flown away.
Had he stayed above 100 feet, as he should have, the airplane would've flown away.
Had the airplane allowed him to exceed alpha max, it would've stalled and crashed anyway.
So, it's not really a case of "airplane didn't respond" - it's far more like Asiana 214. It's a case of "pilot didn't understand his airplane" and flew it into a place (low, slow, engines at idle) where it couldn't be recovered.