Gemara

Mishnah: There was a great Chatzer in Yerushalayim. All the witnesses would gather there, and Beis Din would interrogate them. They made a nice meal for them, to encourage them to come. At first they used to say that a witness (who had left his Techum) may not leave (the Chatzer). R. Gamliel enacted to permit him 2000 Amos in every direction (lest he decide not to come again).

Likewise, the following have 2000 Amos in every direction, like residents of the city (to which they came):

A midwife who left to help deliver, and one who left to save from troops, a river, a house that caved in or from a fire.

Eruvin 44b - Mishnah: If one was permitted to leave the Techum and he found out that the Mitzvah was already done, he has 2000 Amos (from where he was when he found out);

Anyone who leaves the Techum to save may return to his place.

45a - Version #1 - Question: The Seifa permits returning to his house, but the Reisha gives only 2000 Amos!

Answer (Rav Yehudah): The Seifa permits returning with his weapons.

Objection: The question was not difficult at all. Perhaps we are more lenient about one who left to save!

Version #2 (Mishnah): At first they used to say that a witness may not leave (the. Chatzer). R. Gamliel enacted to permit him 2000 Amos.

Likewise, a midwife or one who left to save from troops...is like a resident of the city, and has 2000 Amos.

Question: Is he only like a resident? Our Mishnah permits one who left to save to return to his place!

Answer #1 (Rav Yehudah): Our Mishnah permits returning with his weapons.

Beraisa: At first people (who left the Techum to save) used to leave their weapons in the first house outside the wall. Once, the enemy saw (that they left the wall) and pursued them. Everyone rushed to the house in which the weapons were stored. The enemy followed. Yisraelim were pushing each other. More died through this than by the enemy! They enacted then that people may return with their weapons.

Answer #2 (Rav Nachman bar Yitzchak): If Yisrael won the battle, they may return only 2000 Amos. If the Nochrim won, Yisraelim may return to their original places.

Rishonim

Rif (Eruvin 12a): We establish the Mishnah to permit returning with their weapons.

Rambam (Hilchos Shabbos 27:16): Anyone who had permission to leave the Techum, e.g. witnesses who saw the moon or others permitted to leave for a Mitzvah, has 2000 Amos from where he arrives. If he arrived in a city, he is like residents of the city; he has 2000 Amos in every direction outside the city.

Magid Mishnah: Because he was permitted to leave, it is as if he acquired Shevisah in the city he came to.

Rambam (17): One who left to save Yisraelim from Nochrim, a river, or a house that caved in has 2000 Amos in every direction from where he saved. If the Nochrim were dominant and the Yisraelim are afraid to stay in the place where they saved, they may return to their place on Shabbos with their weapons.

Rosh (Eruvin 4:5): Rav Yehudah says that one may return with his weapons. Rav Nachman bar Yitzchak says that if Yisrael were victorious they may return only 2000 Amos; if not, they may return to their original places. Rabbeinu Meir says that the Halachah follows both of them. It is like Rav Nachman for he is Basra; it is like Rav Yehudah because a Beraisa supports him.

Beis Yosef (OC 407 DH ha'Yotzei): Rav Yehudah did not discuss how far they may return (therefore, he could agree with Rav Nachman).

Poskim

Shulchan Aruch (OC 407:1): If one had permission to leave the Techum, e.g. a midwife who left to help deliver, he has 2000 Amos from where he arrives. If he arrived in a city, he is like residents of the city; he has 2000 Amos in every direction outside the city.

Shulchan Aruch (3): If one left to save Yisraelim from Nochrim, a river, or a house that caved in, he has 2000 Amos in every direction from where he saved. If the Nochrim are dominant and the Yisraelim are afraid to stay in the place where they saved, they may return to their place on Shabbos with their weapons.

Kaf ha'Chayim (13): This means that even if Yisrael was victorious this time, the Nochrim are dominant and the Yisraelim are afraid to stay in the field. An opinion in Hagahos ha'Tur says that one may take his weapons with him only if the Nochrim are dominant. The primary opinion is like the Bach, who permits this in any case.

Kaf ha'Chayim (10): Even if one saw that enough people for the Mitzvah already went and he went also, he is permitted like they are.