A kiln could fire at full rate if a relay locked on, a thermocouple failed, the Kiln Sitter failed, or the contacts in a switch stuck in a single-switch kiln.
Estimate how long your kiln would take to bend the witness cone if for some reason it fired at full rate. Then check the kiln before that critical estimated time. In addition, check the kiln once in awhile just to make sure everything is okay.
Some kilns will not fire hot enough to destroy themselves no matter how long they run. This is especially true for kilns with older heating elements. On the other hand, a cone 10 kiln can get hot enough to melt the ware into a puddle and ruin all the firebricks.
A kiln that has multiple relays is less likely to over-fire than a kiln with a single relay. This is because it would be rare for all the relays to lock on at the same time.