Well - the thing they do is "strain harden" because they start off as soft, annealed metal with few point defects. The problem is that every time they get crushed, the ability to deform is reduced. I remember seeing this demonstration in my Engineering 45 (Properties of Material) class. This one very English materials science professor was famous (some say notorious) for this specific demo. He'd bring out an annealed copper rod and usually ask a smaller female student to bend it, which was pretty easy because it started off soft. Then he'd look for a guy in class who looked to be someone who worked out, and asked him to straighten out the rod. The guy would then try as hard as he could but it wouldn't be able to bend it back because it had work hardened where the crystal structure had deformed and it was considerably stronger than when it was straight.
I've heard of some discussion of annealing an old copper gasket to reuse it. Seems like it would be easier to just get a new one.
This kind of explains it even though it seems to have come from the University of Washington. This is also what happens with cold forging of metals. It doesn't make it stronger, but it makes it far harder to deform later on.
Copper has a cubic crystal structure (Face Centered Cubic) that gives it high ductility. Bending the copper causes work hardening (or strain hardening) because working or straining the copper introduces defects, known as dislocations, into the structure. These defects interfere with further deformation, making the copper harder and stronger, thus making it more difficult to bend further. Copper tubing is used here because it is readily available in hardware stores. Caution must be taken on bending, however, as it can crimp if bent too far too fast. Thus the instruction to bend it slowly. After bending, the materials is harder and thus more difficult to re-bend it to its original condition. The best effect is to have a person of average physical condition do the bending, then ask an obviously strong person to un-bend the copper (this person will typically not be able to get the copper back to its original shape).
Not sure about fiber though. I've used those but were somewhat skeptical about how well they sealed.