I'd have to agree with Mr. Bamboozle whether the failed part is the button fixture on the back of the shoe or the elastic strap from the rear of the sole (it was not completely clear to me..). It's an OEM fix/replace, more likely replace.
Over 7-8 years, 3-4 pairs of Korkers and a couple bazillion hours of service time, I've had one strap fail from tear-though of the slot that holds the button. Not bad for the only part of the system that does not rely on gravity.
I've found Korkers customer service to be pretty good. Depending on the age of the boot, I'll bet they do right by you..