Amud 43a

תוס' ד"ה מי

Is there a slave which cannot be sold for his fine - מי איכא עבדא דלא מזדבן לקנסא

Summary:
People will not be willing to purchase an עבד (who is not worth a שוה פרוטה), even if they don’t feed him, for they do not want him being around, however if it’s only for קנס they may consider paying a פרוטה for the שלשים שקלים. Alternately, if we maintain מכרו לקנס אינו מכור, one cannot sell an עבד who is not worth a שוה פרוטה.

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תוס' ד"ה אם

If you decide to say; in a case where he said; ‘become betrothed to half of me’, she is betrothed - אם תמצא לומר התקדשי לחציי מקודשת

Summary:
The את"ל, in the manner in which the גמרא presents it, is the הלכה.

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תוס' ד"ה ואי

And if you say his betrothal is not a betrothal; how does he have heirs - ואי אמרת קדושיו לאו קדושין יורשין מנא ליה

Summary:
If one is not a בר קידושין anywhere, his progeny do not inherit him.

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