When a Non Jew does something it would work according to Halacha, however when a Jew does the same thing it is useless.
If an animal was mostly slaughtered by a Jew (the majority but not all of the trachea & esophagus were cut) and the animal is not dying, a non-Jew can kill it however he wants and the animal will be kosher. If a Jew shechted the rest of the way, it would be a shihiyah b'miut batra (a pause in the final portion) and the animal is neveila (not kosher). But since the slaughter of a non-Jew is nothing, the majority slaughtered by the Jew is all that counts.
(See Shulchan Aruch YD 23:5)