I'm not familiar with mountain-climbing technique, but I'm guessing this means climbers are always tethered to the cliff by a line, as a basic safety measure. Thus, even if a climber loses his grip and falls, he won't fall to the ground, because he has a line always attached to the cliff. So he'll end up dangling frighteningly from a line, but he'll be safe, and he can then haul himself back up with the line.
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