Many things in applied statistical computing (and computer science in general) is based on approximations. In case of absolute loss function, it has constant decrease rate for loss < 0 and constant increase rate at loss > 0, it neither increases, nor decreases at zero. That's about theory, but in practice, it is unlikely that you will hit exact zero. Moreover, it is not differentiable at zero, but since it is neither increasing, nor decreasing, 0 is a reasonable value to use if we need to choose something for our algorithm to work. If error is equal to zero, then we are done with training and not need to update the weights any more, so this makes perfect sense.