Question: (Beis Shammai said in the Mishnah (above Zevachim 95-1(c)) that charity collectors give the tithed produce to those that do not tithe; and untithed produce to those that tithe; so that everyone ultimately eats tithed produce.) Just because someone is trustworthy and he tithes, why should he lose out by having to tithe and the one who doesn't separate should receive tithed produce?

Answer: The Gabbai bears this in mind and he give the poor Chaver extra so that he will have enough after he tithes.

Question: Why is Beis Shammai (strict only to give tithed produce to one who doesn't tithe, if they said in the Mishnah that one may give Demai to the poor)?

Answer: Here, it refers to the poor of the town, so the problem can be prevented by only giving them tithed produce. But earlier, the Mishnah was discussing travelling poor people - even if you tithe it for them here, they will ultimately receive untithed produce if they go to a town with Gabbaim who are Amei HaAretz.

Question: Why don't the Chachamim accept this?

Answer: If you probe into the status of the donor, you will reduce the amount of charity given (as the Gabbai will be so busy with the issue of Demai, he will have less time to actually collect and distribute charity).

Tosefta: On Yom Tov, the Gabbaim don't announce the same way that they announce during the week; they collect and distribute in private and within each neighborhood separately.

In Sheviis, the Gabbaim should not be particular to avoid collecting money from those who eat produce of Sheviis.

If they donated bread, it is permitted, because they would only give money or eggs to others without knowing that these can receive the Kedusha of Sheviis (but they would inform the recipient if they were giving Sheviis bread).

(R. Chanina citing R. Pinchas): When are they not suspected (for things other than money and eggs)? In a place where they are suspected of only planting but not of eating - since they wouldn't eat themselves, we are not concerned that they would give others.

(Tosefta continues): Kohanim who make dough in Taharah (from grains received from Amei HaAretz and separate their Challah for them) should not be particular to avoid doing this for those who eat produce of Sheviis.

Some have a text in the Tosefta: They should be particular (to avoid doing this for those who eat produce of Sheviis).

(R. Pinchas): For those that have the text 'they should be particular', it's because of the concern that this prohibited Challah will become mixed up with other Challah. For those that have the text 'they should not be particular', it's because otherwise, by not separating Challah for them, you are driving them from the lenient (Sheviis) to the stringent (Tevel). Tevel is stringent because one who eats it incurs death from Heaven. Sheviis is lenient because it is merely a negative commandment.

Question: (According to those that have the text 'they should not be particular') what should he do?

Answer (Rav Chuna): He should bring a Kohen who is suspected in Sheviis and have him immerse and give him that Challah to eat.

Question: Isn't he giving Taharos to an Am HaAretz (and maybe he won't wait until after nightfall, as required, before he eats it)?

Answer (R. Mana): He should bring a Kohen who is suspected in Sheviis and have him immerse and watch him until evening and then give him the Challah.

Question: Doesn't this encourage sinners (as you are only giving him the Challah because he isn't careful about Sheviis)?

Answer (R. Shimon ben Kani citing R. Acha): Rather, he should keep the Challah until Erev Pesach and then burn it.