Summary

Yosef Karo Shulchan Aruch — Yoreh Deah 2 Whether slaughter performed by a non-Jew or a mumar…

Seif 2 A mumar/ wanton sinner who eats nevelot deliberately, a Yisrael can check the knife and give him it, then it's permitted to eat from his shechita, even if he shechts just for himself. Provided he knows the laws of shechita. But if he did not check for him the knife initially, it's forbidden to eat of his shechitah until he checks it afterwards. And he should not be given to shecht initially even with a kosher person standing over him without checking [the knife] for him [but just relying that] the knife is kosher based on checking it afterwards.
Source: Wikisource

Yosef Karo Shulchan Aruch — Yoreh Deah 2 Whether slaughter performed by a non-Jew or a mumar…

Whoever shechted and a treifah once came out from under his hand, if that's not muchzak/ an established pattern then it's permitted to eat from his later shechitah. However, this is determined by the dayan/ judge's eyes' view of the man shechting. If he's already faulty and accustomed to do this we remove him.
Source: Wikisource

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