Yoreh Deah Siman 21 Seif 5

ה הָיָה חֲצִי הַקָּנֶה חָתוּךְ, וְשָׁחַט בּוֹ וְהִשְׁלִימוֹ לְרֹב, כָּשֵׁר; וְכֵן אִם הִתְחִיל לִשְׁחֹט בַּמָּקוֹם הַשָּׁלֵם, וּפָגַע בַּחֲתָךְ, וְהֶחָתוּךְ מַשְׁלִימוֹ לְרֹב, כָּשֵׁר.

 

Seif 5

If 1/2 of the esophagus was cut, and then it was slaughtered completely to a sizable amount it is complete; it is permissible.

 

Thus (in a case) where if one started slaughtering in a spot (in the sign) that is whole, and one found their was a flaw in the (original) cut, and one cut it completely to a sizeable amount, it is acceptable.