Yevamos, Chapter Fifteen, Mishnah Ten. The Mishnah opens with the words: "Halchah liyavam bimdinas hayam" - a woman who went overseas with her husband, and at the time she left her husband had no brothers at all. She therefore left with the presumption that if her husband would die, even though he had no children, there would be no one to perform yibum with her, and she would be permitted to marry anyone.
Now the woman comes back and claims: "Meis baali v'achar kach meis yevami" - my husband died and afterward my brother-in-law died, or "Meis yevami v'achar kach baali" - my brother-in-law died and afterward my husband.
It is worth noting that in this case the order makes no difference. The reason the Mishnah presented both versions is that in the earlier Mishnayos, where there was a difference regarding the child, both versions were presented, and so it presented them here as well. Either way, her claim is that the brother-in-law died.
The ruling - she is believed: We believe her, since she left with the presumption that she has no brother-in-law at all. She is the one who informed us that a brother-in-law exists, meaning she is the one who created the problem. And since our entire knowledge of his existence comes from her mouth, she also has the power to undo it and say that there is no longer a brother-in-law.
The second case - she, her husband and her brother-in-law went overseas:
Here she had a brother-in-law even before they left, and the brother-in-law went with her and her husband overseas. She comes back and says: "Meis baali v'achar kach meis yevami" - my husband died and afterward my brother-in-law died, or "Meis yevami v'achar kach baali" - my brother-in-law died and afterward my husband. Either way her claim is that the brother-in-law died as well, except that here we are dealing with a brother-in-law whose existence was known to us from the outset.
The ruling - she is not believed: She may not marry anyone else. As far as we are concerned, it is established that she has a brother-in-law, and she must find him and bring him back from overseas so that he can perform yibum or chalitzah. Until it becomes clear what became of the brother-in-law, she is not permitted to marry.
The reason for this, as the Mishnah concludes:
"She'ein ha'ishah ne'emenes lomar meis yevami shetinasei" - a woman is not believed to say that her brother-in-law died so that she may marry.
"V'lo meisah achosi shetikanes l'veisah" - she is likewise not believed to say that her sister died so that she may enter her house, meaning so that she may be permitted to marry her sister's husband.
"V'ein ha'ish ne'eman lomar meis achi sheyeyabem ishto" - a man is not believed to say that his brother died so that he may perform yibum with his wife.
And likewise he is not believed to say that his wife died so that he may marry her sister. These claims we do not permit.
A special leniency was given only to a woman who says that her husband died, and for two reasons: because a woman is meticulous and investigates thoroughly before she remarries, and because of the concern that she will remain an agunah. After all, the only man in the world permitted to her is her husband, and when she cannot locate her husband she is left an agunah. Therefore they were more lenient with her, combined with the fact that she herself will investigate the matter properly.
In summary: When the woman left with the presumption that she has no brother-in-law and she herself testifies both to his existence and to his death, she is believed, since the mouth that forbade is the mouth that permitted. But when the brother-in-law was established before us, she is not believed to say that he died, for a woman is not believed to say "my brother-in-law died" in order to marry, nor is she believed about her sister's death, and likewise a man is not believed about the death of his brother or his wife in order to permit himself. The special leniency was stated only regarding a woman's testimony about her husband's death, because of her thoroughness and the concern for iggun.