Yevamot, Chapter Fifteen, Mishnah Eight
Our mishnah deals with a situation where a woman goes abroad with a husband and a son and then returns claiming that both have died. The question is: is she liable for yibbum.
1) A woman who went with her husband to a country beyond the sea, and her son was with her, and who came back and stated, my husband died and afterwards my son died, is believed.
2) [If she stated] my son died and afterwards my husband died, she is not believed, but we are concerned that her words [might be true] and she must, therefore, perform halitzah but may not contract yibbum.
Section one: If her husband died before the son died, then at the point of death she was not liable for yibbum (for her husband died at a point when he had kids). Since she went abroad under the assumption that she is not liable for yibbum, and she now returns claiming that this is still true, she is believed. This mishnah works according to a well-known principle whereby a person is believed if he does not change the status quo, but not necessarily believed if he does change it.
Section two: In this case, she claims that the son died first and therefore when her husband died he had no children, leaving her liable for yibbum. Since she is changing the status quo that existed when she left, and now claiming that she is liable for yibbum, she is not entirely believed and she is not allowed to contract yibbum with her dead husbands brother. However, since she might be telling the truth, and really be liable for yibbum, she first must perform halitzah and only then is she allowed to remarry.