Gemara

60b (Mishnah): If one put an Eruv outside [the Ibur], whatever he gains, he loses.

Question: He loses more than he gains!

(Beraisa): If one put an Eruv outside the Ibur [e.g. to the east], even one Amah outside, he gains that Amah [to the east], but [to the west] he loses [it and the width of] the entire city. Its true measure is deducted from the 2000 Amos that he may go [to the west].

Answer: The Mishnah discusses when his 2000 Amos extend pass the city. The Beraisa discusses when his 2000 Amos end in the city:

(R. Idi citing R. Yehoshua ben Levi): If Reuven [lodged outside a city, and] counted his steps and found that his 2000 Amos end in the middle of the city, he may go only up to there;

If his 2000 Amos contain the end of the city, the entire city counts like only four Amos, and he counts the rest of his 2000 Amos past the city.

Objection (R. Idi): What is the difference whether his 2000 Amos extend pass the city or end in the city?!

Defense (Rava): Both of these are learned from a Mishnah!

(Mishnah): [If a big city and a small city are less than 2000 Amos apart,] people of the big city may traverse all of the small city [without deducting from their 2000 Amos,] but people of the small city may not traverse all of the big city.

This is because the 2000 Amos of someone in the big city extend past the small city, but the 2000 Amos of someone in the small city end in the middle of the big city.

R. Idi questioned the law, for his text in the Mishnah said in both cases that people of' one city may traverse all of the other city.

Rishonim

Rif (18b) and Rosh (5:12): If one put an Eruv 1000 Amos east of the city, he may walk 3000 Amos to the east and 1000 Amos to the west. He gained 1000 Amos to the east and lost 1000 Amos to the west. All Rabanan rule like R. Yehoshua ben Levi. Even though R. Idi was astounded, we are not concerned for this, for Rava derived from the Mishnah like this.

Rambam (Hilchos Eruvin 6:2): The next day, he may walk 2000 Amos from his Eruv in every direction. When he walks from his Eruv to the city, he may walk in the city only until the end of his 2000 Amos. If the city is contained within his 2000 Amos, the city is considered like only four Amos, and he completes his Shi'ur outside the city.

Rambam (Hilchos Shabbos 27:5): If one walks his 2000 Amos and they ended in a Dir, Sahar, cave or city, he may walk only until the end of the 2000 Amos. We do not say that since they ended in a Reshus ha'Yachid, he may traverse the entire Reshus ha'Yachid. This is when his 2000 Amos end in the middle of a cave or city. If the Reshus ha'Yachid is contained within his 2000 Amos, the entire Reshus is considered like four Amos, and he completes the rest outside of it.

Rambam (6): If one was 1000 Amos from his Shevisah, if (Chazon Ish - the text should say or) outside the city [1000 Amos] from the city or a cave at most 1000 Amos long, he may traverse the entire city or cave, and outside of it 996 Amos.

Rosh (ibid.): When his 2000 Amos end in the middle of the city, he loses the other half of the city.

Poskim

Shulchan Aruch (OC 408:1): If one left the city on Erev Shabbos and put food for two meals outside the city within the Techum and fixed his Shevisah there, even if he returned to his city and lodged in his house, it is as if he dwelled where he left the food.

Mishnah Berurah (5): This means that he returned to the city during the day. If he remained outside until night, he need not put food at all (409:7)!

Shulchan Aruch (ibid.): He may walk from his Eruv 2000 Amos in every direction. Therefore, when he walks towards his city the next day, he may go only until his measure finishes. If the city is contained within his measure, it is all considered four Amos, and he completes the Shi'ur outside the city. If he put an Eruv 1000 Amos east of his house, the next day he may walk 2000 Amos to the east of his Eruv, and 2000 Amos to the west, i.e. 1000 Amos to his house, and 1000 Amos past his house within the city. He may walk in the city only until the 1000 Amos.

Beis Yosef (DH u'Mah she'Chasav Aval): The Tur brings from the Rambam that he has only four Amos in the city itself.

Hagahos Tur ha'Shalem (7', citing Derech Tamim 9): The Rambam says that he gets until the end of his 2000 Amos! The Tur must mean that if he goes past the 2000 Amos, he has only four Amos, like one who left the Techum. However, this is difficult, for this is obvious!

Beis Yosef (ibid.): The Tur disagrees, for if so, one who lives in a big city and put an Eruv outside cannot return to his house! I.e. if so, no one in a big city would ever make an Eruv, lest he lose his city. This is not difficult. If he needs to walk in the direction in which he is Me'arev, he will make an Eruv, even though he loses his city! In any case Hagahos Maimoniyos brought from Semak like the Tur, and so explained Rashi. We say that he has only half the city, i.e. even if he lodged in it, i.e. he may not go past the city. He may go in the entire city, since he lodged in it. Smag wrote Stam like R. Yehoshua ben Levi, which connotes like the Rambam.

Gra (DH v'Eino): The simple reading of the Gemara connotes like this. He loses the entire city. If one may walk the entire city, he loses only the extra distance of the Eruv from the city! The Tosefta (8:1) connotes like this. Tosfos must say that this is when he did not lodge in his house.

Mishnah Berurah (7): His primary Shevisah is in the place of the Eruv. Therefore, if he wants to return to his city, he may walk only until his 2000 Amos end. Even if he did not leave his house yet, if he is more than 2000 Amos from his Eruv, he may not go even one Amah in the other direction, even within his city. Even if he reconsidered [and does not want Shevisah in the place of his Eruv], it does not help.

Kaf ha'Chayim (10): If Nochrim took him in the city past his 2000 Amos, he has only four Amos.

Shulchan Aruch (ibid.): If from his house until the end of the city is less than 1000 Amos, even one Amah less, the entire city is considered four Amos, and he may walk outside it another 996 Amos to complete the 2000. Therefore, if he put the Eruv 2000 Amos from his house, he lost the entire city. He may not go in the city west from his house even one Amah.

Beis Yosef (DH u'Mah she'Chasav): The Tur and Rambam say that when the city is included in his 2000 Amos, he gets another 1996 Amos outside the city. This is unlike R. Yehonason (18b DH ha'Nosen), who says that even though we say that the entire city is like four Amos, this does not mean that it counts like four of his 2000 Amos, and he loses them in the other direction. Rather, it means that the city is not part of the calculation [of 2000], even though we gave four Amos for the place he put his Eruv.

Mishnah Berurah (10): When the Eruv is 2000 Amos from his house, even though it is less than 2000 Amos from the city and he may walk to it, he may not return after dark and lodge in his house. He must lodge in a house within 2000 Amos of his Eruv.

Rema: Some say that even if his measure finished in the city, he may walk in the entire city, but not outside it. One may be lenient.

Mishnah Berurah (11): This opinion holds that even though his Eruv was more than 2000 Amos from his house, since he lodged in the city, the entire city is considered four Amos. Therefore, he may walk in the entire city, and all the more so return to his house. Also this opinion agrees that the city counts towards 2000 Amos, so he may not leave the city at all on the opposite side of his Eruv. If he lodged in the place of his Shevisah and his 2000 Amos ended in the city, or he lodged in the city and his 2000 Amos ended in another city, all agree that he may walk only until his 2000 Amos end.

Mishnah Berurah (12): Also the Bach and other Acharonim say that one may be lenient.

Kaf ha'Chayim (11): Eliyahu Rabah says that one may be lenient because also the Rambam in Perush ha'Mishnayos wrote like the Tur.

Kaf ha'Chayim (14): Eshel Avraham says that several hold like the Rambam, so one should be stringent. I say that many hold like the Tur, so one may be lenient in pressed circumstances for a great need.

Rema (ibid.): If his measure finished at the end of the city, even though there is an Ibur in front of the city, the entire city is considered four Amos. We do not consider the Ibur to be like the city to be stringent.

Mishnah Berurah (13): We do not say that if his 2000 Amos do not contain the Ibur, it is as if they finish in the middle of the city. The Ibur is a leniency for the measure of the Techum. It is not a stringency. However, we count the Ibur with the city to be like four Amos only if his 2000 Amos extend to the end of the Ibur.