If a commercial airliner enters into a spin at high altitude, is it possible to recover?
How to stabilize a spinning aircraft

Stabilizing a spinning aircraft is fairly easy. If the center of gravity is not too far forward, the rudder is deflected in spin direction and the elevator fully up (adjusting the horizontal tail trim helps, too), the spin will continue until the aircraft hits the ground. In some cases, the spin might oscillate between two stable modes, and the aircraft will continuously pitch up and down between them. An airliner with its high wing loading will loose a couple of hundred meters per turn in a spin, but will not accelerate once the spin has fully developed. Increasing air density on the way down will actually decrease the rate of descent.

But I guess you wanted to ask something entirely different.

Ending a spin

Ending the spin is equally easy and is performed by the opposite commands which stabilize the spin. Proving that the aircraft will easily come out of a spin is actually part of certification requirements. The stable rate of descent gives the pilots ample time to end the spin, and even if the engines have failed, emergency systems will ensure that the pilots can control the aircraft. The risk that an otherwise normal flight will end in an unrecoverable spin is practically zero.

I would actually prefer that the airplane enters a spin. If the center of gravity is in the forward part of the allowed range, it is more likely that it will enter a spiral dive after stalling. Now the pilots need to react quickly and with measure, because drag is much lower in a spiral dive than in a spin, and the resulting higher speed poses a real danger. For that reason the flight control system in the type of aircraft you mentioned, the A-320, will prevent the aircraft from entering a spiral dive in the first place.

What if something snaps?

So far, we have assumed that all systems work. What if something snaps? The surprising answer is: Mostly nothing. A fundamental design principle for aircraft demands that primary structural parts or equipment can snap without the aircraft breaking apart. This is called redundancy: Every primary structure and every flight-critical piece of equipment is duplicated, so if one part breaks, the other, redundant part will continue to carry the loads and the flight can be terminated as planned. Regular inspections make sure that such damage is caught quickly, and the manufacturers continue to improve the existing fleet once a weakness has been spotted.

Even if something snaps, it is extremely unlikely that the aircraft will enter a spin, and even if this happens, it is easy to end. Your fears are unfounded.