In Yoma on 67a, in the middle, it talks about the where the strip of red wool should be tied before sending the goat off the side of the mountain.
As far as I understand (and with the help of the Artscroll's commentary), it is saying that half of the strip should be tied to the rock and half to the goat's horns.
This appears to be because "when the strip turns white, the designee may be satisfied that atonement has been achieved, and he may neglect to push the Azazel goat off the cliff." (Rashi + Artscroll)
My question is: How could such an instance possibly happen? Isn't the change of color of the wool a miraculous occurrence? It is not like it is a "natural" function of atonement that wool should turn from red to white. And if it is something miraculous, we understand that it is beyond nature and certainly something that Hashem would not let happen a second too early or a second too late. So, how could the Gemara even consider the possibility that the strip would change color before the person with the goat has finished his duty?
And, I suppose a second, related question is: If the strip did turn white before he pushes the goat, then what purpose need he continue to do the Azazel service? It seems like atonement has been achieved.