Talmud for Yevamot 10:1
הָאִשָּׁה שֶׁהָלַךְ בַּעְלָהּ לִמְדִינַת הַיָּם, וּבָאוּ וְאָמְרוּ לָהּ, מֵת בַּעְלֵךְ, וְנִסֵּת, וְאַחַר כָּךְ בָּא בַעְלָהּ, תֵּצֵא מִזֶּה וּמִזֶּה, וּצְרִיכָה גֵט מִזֶּה וּמִזֶּה. וְאֵין לָהּ כְּתֻבָּה וְלֹא פֵרוֹת וְלֹא מְזוֹנוֹת וְלֹא בְלָאוֹת, לֹא עַל זֶה וְלֹא עַל זֶה. אִם נָטְלָה מִזֶּה וּמִזֶּה, תַּחֲזִיר. וְהַוָּלָד מַמְזֵר מִזֶּה וּמִזֶּה. וְלֹא זֶה וָזֶה מִטַּמְּאִין לָהּ, וְלֹא זֶה וָזֶה זַכָּאִין לֹא בִמְצִיאָתָהּ וְלֹא בְמַעֲשֵׂה יָדֶיהָ, וְלֹא בַהֲפָרַת נְדָרֶיהָ. הָיְתָה בַת יִשְׂרָאֵל, נִפְסְלָה מִן הַכְּהֻנָּה, וּבַת לֵוִי מִן הַמַּעֲשֵׂר, וּבַת כֹּהֵן מִן הַתְּרוּמָה. וְאֵין יוֹרְשִׁים שֶׁל זֶה וְיוֹרְשִׁים שֶׁל זֶה יוֹרְשִׁים אֶת כְּתֻבָּתָהּ. וְאִם מֵתוּ, אָחִיו שֶׁל זֶה וְאָחִיו שֶׁל זֶה חוֹלְצִין וְלֹא מְיַבְּמִין. רַבִּי יוֹסֵי אוֹמֵר, כְּתֻבָּתָהּ עַל נִכְסֵי בַעְלָהּ הָרִאשׁוֹן. רַבִּי אֶלְעָזָר אוֹמֵר, הָרִאשׁוֹן זַכַּאי בִּמְצִיאָתָהּ וּבְמַעֲשֵׂה יָדֶיהָ, וּבַהֲפָרַת נְדָרֶיהָ. וְרַבִּי שִׁמְעוֹן אוֹמֵר, בִּיאָתָהּ אוֹ חֲלִיצָתָהּ מֵאָחִיו שֶׁל רִאשׁוֹן פּוֹטֶרֶת צָרָתָהּ, וְאֵין הַוָּלָד מִמֶּנּוּ מַמְזֵר. וְאִם נִסֵּת שֶׁלֹּא בִרְשׁוּת, מֻתֶּרֶת לַחֲזֹר לוֹ:
If a woman's husband went abroad, and they came and said to her [i.e., if one witness said to her]: Your husband died, and she remarried [on the testimony of one witness], and then her husband returned, she leaves the one and the other [as per the halachah of a married woman who committed adultery, who is forbidden to both her husband and to the adulterer, not having been forced. And though the rabbis accepted one witness to prevent agunah (perpetual inability to remarry), that is because a woman is expected to thoroughly search out the matter before she remarries, and because she did not do so in this instance, she is penalized. But if she remarried on the testimony of two witnesses who said: Your husband died, it is stated at the end: "If she remarried without a ruling of beth-din (i.e., if the permission of beth-din were not required, two witnesses having testified), she is permitted to return to her first husband," being considered "forced," for what was she to have done? But in the gemara it is shown that this is not the halachah, that it makes no difference whether she remarried by the ruling of beth-din on the testimony of one witness, or on the testimony of two witnesses — if her first husband returns, she leaves both, and all of the other provisions apply to her], and she requires a get from the one and from the other. [The reason she requires a get from the second is that when the second is seen alive, people think that she received a get from the first, on the basis of which she married the second, so that she is his bona fide wife; and if he sends her away without a get, it is found (i.e., the impression is given) that a married woman is sent away without a get.] And she has neither kethubah, nor fruit, nor sustenance, nor belaoth, [which were lost; but she does not forfeit those which remain] — neither from the one nor from the other. If she had taken from the one or from the other, she must return it, and the child is a mamzer from the one or from the other [If she had a child by the second, it is a confirmed mamzer, and if the first took her back and she had a child, it is a mamzer by rabbinic ordinance.], neither of them (if they were Cohanim) may become unclean to her (if she died), neither acquires the lost objects that she finds [For why did the rabbis ordain that a husband acquires such objects? To prevent his hating her. But here, let him hate her by all means!], nor the work of her hands [For why did the rabbis ordain that a husband acquires this? Because he feeds her. But in this instance, since her sustenance is not incumbent upon him, he does not acquire the work of her hands.], nor (the power) to absolve her vows. [For why does a husband have such power? So that she not become demeaning to him. But here, let her become demeaning by all means!] If she were the daughter of an Israelite, she becomes unfit for (eating) terumah, [having the status of a "zonah"], and if she were the daughter of a Levite (she becomes unfit for eating) ma'aser [This is a (rabbinic) penalty, for (by Torah ordinance), the daughter of a Levite who became a zonah does not become unfit for eating ma'aser], and the daughter of a Cohein (becomes unfit for eating) terumah [even that which is terumah by rabbinic ordinance], and the heirs of both do not inherit her kethubah [a kethubath b'nin dichrin (see Kethuboth 4:10)]. And if they died, the brothers of the one and the brothers of the other give chalitzah and do not take her in yibum. [The brothers of the first give chalitzah by Torah ordinance, and the rabbis decreed that yibum not be performed; and the brothers of the second give chalitzah by rabbinic ordinance, just as she requires a get from the second by rabbinic ordinance.] R. Yossi says: Her kethubah is attached to the property of her first husband. R. Elazar says: Her first husband has rights in what she finds, the work of her hands, and the absolution of her vows. R. Shimon says: Cohabitation with or chalitzah from the brothers of the first exempt her tzarah. [He disagrees with what precedes, viz.: "They give chalitzah and do not take her in yibum], and the child is not a mamzer [if her first husband took her back. And the halachah is in accordance with neither R. Yossi, nor R. Elazar, nor R. Shimon.] And if she married without the permission [of beth-din, as when two witnesses said to her: Your husband died, in which instance the permission of beth-din is not required], she is permitted to return to him.