Yevamos, Chapter 15, Mishnah 9. This mishnah deals with the same case discussed in the previous mishnah - a woman who went overseas with her husband - except that here no son went out with them. She left with the presumption that she was childless, since her husband had no children. Now she returns and testifies that her husband has died, and she adds: "Nitan li ben bimdinas hayam" - a son was born to her overseas. The question is how this testimony affects her obligation of yibum, and that depends on the order of deaths that she reports.
The first claim: "My son died and afterward my husband died":
According to this order, the son died first and the husband after him, so that at the time of the husband's death he had no son - and therefore she is obligated in yibum. About this the mishnah says: "Ne'emenes" - she is believed.
The reason: she left here with the presumption that if her husband were to die she would be obligated in yibum, since he had no child. Now she tells us that a son was born, but this is the principle of "the mouth that forbade is the mouth that permitted": she is the one who informed us of the existence of the son, which in itself is the problem that would bar yibum, and she is the one who informed us that the son died first. Since our knowledge of that problem comes from her words alone, we believe her as well when she says that the son died first and that there is therefore no impediment. The result is that she stands in exactly the same status in which she left here, and she is obligated in yibum.
Therefore she is permitted to undergo yibum with the brother-in-law, and she may not marry anyone else unless she receives chalitzah.
The second claim: "My husband died and afterward my son died":
According to this order, she left without a son, a son was born to her overseas, and the husband died first and the son after him. By her account she is not subject to yibum at all, and there would seem to be room to permit her to marry anyone. But the mishnah rules: "Einah ne'emenes" - she is not believed, because her words contradict the presumption in which she has been held until now, that she is obligated in yibum.
Nevertheless, "v'choshshin l'divareha" - we take her own claim into account, and from here comes the halachah: "v'choletzes v'lo misyabemes" - she performs chalitzah and does not undergo yibum:
Chalitzah: because of the presumption that she is bound to the brother-in-law, we require chalitzah of her.
Yibum: we do not permit her to undergo yibum, since according to her words there was a son at the time of her husband's death, and by her own account she is forbidden to the brother-in-law.
In summary: a woman who left with the presumption of being childless and testified that a son was born to her overseas - if she said "my son died and afterward my husband died," she is believed by virtue of the rule "the mouth that forbade is the mouth that permitted," and she undergoes yibum. But if she said "my husband died and afterward my son died," she is not believed against the presumption, yet we take her words into account: she performs chalitzah and does not undergo yibum.