To answer your original question, they absolutely can burst or wear. In fact, anytime you roll by a car that has a constantly bouncy wheel while at constant speed, that's the damper low on pressure or completely shot.
I just replaced my stock dampers and lowering springs with coilovers since my car was due for some needed suspension love anyways. Oddly enough, I was considering getting Koni yellows until I heard about the installation process and then decided against it and to just spend more money on what I would consider a more proper setup.
Riding on dampers that aren't properly cushioning impacts will generate extra pressure on your wheels when you ride over a bump of any significance. Any time excessive force is applied to your wheels this will cause cracks to form in slight imperfections if they are alloy rims. Also, this translates into extra wear on everything else in your suspension (control arms, tie-rods, bushings, steering column) and drivetrain (if you drive a rear wheel drive vehicle with your rear dampers busted), as well as throw your alignment off track faster than normal equalling faster tire wear.
I'll be curious to see how Koni takes care of this. I've generally heard good things about the quality of their product. Hope they resolve this quickly for you!