Gemara

55b (Beraisa): At first, they said that one may not stomp with a Yisrael who allows the wine to become Tamei, for one may not help transgressors (one may not be Metamei Chulin in Eretz Yisrael).

They retracted to forbid even harvesting with such a Yisrael, and all the more so one may not stomp with him.

Gitin 61a (Mishnah): If Leah is suspected to transgress Shemitah, Sarah may lend to her a sifter, grinder or oven. She may not sift or grind with her.

Sarah, an Eshes Chaver (her husband is trustworthy about tithes or Taharah) may lend to Leah (a commoner's wife) a sifter, and she may sift and grind with her. Once she adds water (e.g. to knead), Sarah may not help, for we do not assist transgressors. The Heter was only for the sake of Shalom.

We encourage Nochrim working in Shemitah, but not Yisre'elim.

Question: Why do we forbid helping sift or grind in the Reisha, but permit this in the Seifa?

Answer #1 (Abaye): Most commoners tithe properly.

Answer #2 (Rava): The Seifa refers to helping someone reliable about tithes, but not about Taharah. Since the Isur be Metamei Chulin in Eretz Yisrael is only mid'Rabanan, we are more lenient. The very Seifa (once she adds water, Sarah may not help) discusses Tum'ah of Chalah, which is mid'Oraisa.

Shabbos 2a (Mishnah): If an Ani takes a basket from the hand of a Ba'al ha'Bayis in his house, and took it outside, he is liable and the Ba'al ha'Bayis is exempt.

3a: Here, 'exempt' means permitted.

Rishonim

Rambam (Hilchos Ma'aser 10:13): If a Chaver doctor was feeding a sick commoner (suspected not to tithe) the commoner's food, he puts it into the Choleh's hand, but not into his mouth. If the food is of the doctor, he may not put it even in his hand. Likewise, if he knows that the (Choleh's) food is Vadai not tithed, he may not put it even in his hand.

Kesef Mishneh: This is from the Yerushalmi. Chachamim did not decree against putting the food in the Choleh's hand, for it is the Choleh's food and it is a Safek and he could take it himself and the doctor did not nothing. One may not put Vadai Tevel in his hand, for this is helping transgressor. Similarly, if it is the doctor's Demai, a Chaver may not feed someone food that was not Vadai tithed.

Rosh (1:2): Why did the Beraisa discuss giving wine to a Nazir, rather than giving a Neveilah to a Yisrael? This is because a Nazir is not careful not to drink it, for he drank all his life and he sees others drinking, therefore, even if he asks Stam one may not give to him, lest he forget his Nezirus and drink. Stam, one may give a Neveilah to a Yisrael, unless he knows that he surely wants to eat it. Therefore, one may not give Isur to a Mumar, even if it is the Mumar's, if he is on the other side of the river.

Rosh and Ran (Shabbos 1:1 and 1a DH u'Makshu): Why may David (the Ba'al ha'Bayis) let the Ani take the basket? He transgresses Lifnei Iver, like one who gives wine to a Nazir! Do not say that the Ani could take it even if David did not give it to him, for still David transgresses Lifnei Iver mid'Rabanan. Even when a minor eats Neveilah, Beis Din must stop him, all the more so one may not help an adult to sin! Rather, there is no Isur Shabbos, but indeed it is forbidden due to Lifnei Iver.

Rashi (Gitin 61a DH Rov): Abaye holds that since most commoners tithe properly, the concern is only mid'Rabanan. For Darchei Shalom, one may help transgressors. 'One who is suspected about Shemitah' connotes that she is established to be suspected (the concern is mid'Oraisa).

Rashi (61a DH Rava): Rava holds that it is an even Safek whether commoners tithe. It is a mid'Oraisa concern, so one may not help. Rather, the Seifa discusses concern for being Metamei Chulin in Eretz Yisrael, which is only mid'Rabanan, so one may help transgressors for Darchei Shalom.

Tosfos (Gitin 61a DH Mash'eles): Why do we need to permit lending Kelim due to Darchei Shalom? We can be Toleh (ascribe) that she needs the Keli for permitted grain, like we say in Shevi'is (5:6)! We permit selling Kelim that can be used for Heter or Isur. We forbid only Kelim used only for Isur. Beis Hillel permit selling a plowing cow in Shemitah, for the buyer could slaughter it (Shevi'is 5:9)! Avodah Zarah 15b learns from there that one may sell a cow to a Nochri, and be Toleh that he will slaughter it. That Heter is not due to Darchei Shalom, for Darchei Shalom does not apply to sales. Even if it applied to sales, lest it look like he refuses to sell because he suspects him, this is only for selling to a Yisrael! Also, the Gemara there did not mention Darchei Shalom. R. Tam says that here we know that she has no permitted grain, therefore, we permit only due to Darchei Shalom. Darchei Shalom does not apply to a sale, therefore, one may not sell if we cannot be Toleh. The Yerushalmi discusses being Toleh on using a sifter to count coins, a sieve to sieve sand, or an oven for flax. This connotes that the borrower has no permitted grain to be Toleh on. It is a weak Teliyah, so we permit only due to Darchei Shalom. Selling a cow because it could be slaughtered is a good Teliyah; it permits even without Darchei Shalom. Even though the Reisha discusses Vadai Shemitah, the Gemara asked from the Seifa, for it assumes that Peros of someone suspected are considered Vadai Tevel.

Tosfos (Avodah Zarah 55b DH Ein): The Beraisa forbids even finishing stomping with a Yisrael, even though the Peros are already Tamei, for he helps transgressors.

R. Shimshon (Shevi'is 5:9): The Yerushalmi asked whether everything in our Perek, e.g. selling a plowing cow or Peros, lending measures, changing money...) is permitted due to Darchei Shalom, or only the last case (lending Kelim to a woman suspected about Shemitah). It answered that the other are not due to Darchei Shalom, for they were not taught in Gitin with enactments for Darchei Shalom. R. Mana held that Darchei Shalom permits lending Kelim even though they are surely for Isur. We find that one who does not lend Kelim gets a bad reputation (Kesuvos 72a). R. Ze'ira said that we permit only Stam, for we may be Toleh that they will be used for Heter.

Poskim

Shulchan Aruch (OC 347:1): If Ploni took a basket from David standing in the house and brought it out to Reshus ha'Rabim, Ploni is liable, and David is exempt, but it is forbidden.

Magen Avraham (4): David transgresses Lifnei Iver. If the basket was resting in a way that Ploni could take it even if David did not give it to him, he did an Isur mid'Rabanan. Even when a minor eats Neveilah, Beis Din must stop him, all the more so one may not help an adult to sin, like the Rosh says. See Siman 343 (below). The Yerushalmi forbids lending Kelim used for Melachah to someone suspected of doing Melachah on Shabbos, unless we may ascribe that he will use it for a permitted Melachah. It must be something common, unless we lend for the sake of Shalom. It is Derech Eretz to bless someone working that he succeed, but if he engages in Isur, it is forbidden.

Eshel Avraham (OC 163:2): Lifnei Iver is a Lav, and helping transgressors is mid'Rabanan. Based on this, for an Isur mid'Rabanan, if they are on different sides of the river, Chachamim decreed like Torah law and he transgresses Lifnei Iver mid'Rabanan. However, helping transgressors do an Isur mid'Rabanan is like a decree for a decree (and Chachamim did not forbid this). The Rambam says 'similarly, if it is Vadai Tevel he may not give to him.' Regarding Vadai Tevel there is an Isur mid'Rabanan of helping transgressors. For Demai Chachamim did not decree, but in any case one may not put in his mouth. Regarding the doctor's Demai, Lifnei Iver applies mid'Rabanan. It seems that one may put in his hand, for we do not forbid helping transgressor for an Isur mid'Rabanan. Similarly, one may put food in the hand of one who will not wash if it belongs to the eater and he could take it himself. If the Choleh is not dangerously sick, he can separate the tithes, and even if he does not, mid'Rabanan laws are permitted for him.

Shulchan Aruch (343:1): If a minor eats Neveilah, Beis Din need not stop him, but his father must rebuke him or stop him. One may not feed him even an Isur mid'Rabanan. One may not accustom him to transgress even mid'Rabanan Isurim of Shabbos or Yom Tov.

Rema: Some say that if reached the age of Chinuch, we must stop him. Some say that Chinuch applies to only to the father, but not to Beis Din.