Yevamot, Chapter Fifteen, Mishnah Ten
This mishnah continues to discuss women who return from being abroad and come back and testify that their husbands and in this case brothers-in-law have died.
1) [If a woman states] a brother-in-law was given to me [while I was] in a country beyond the sea, and afterwards she states, my husband died and afterwards my brother-in-law died or my brother-in-law died and afterwards my husband died, she is believed.
2) If a woman and her husband and her brother-in-law went to a country beyond the sea, and she [on returning home] stated, my husband died and afterwards my brother-in-law [died] or my brother-in-law [died] and afterwards my husband [died] she is not believed;
a) For a woman is not to be believed when she asserts my brother-in-law is dead, in order that she may marry again;
b) Nor [is she believed when she states that] her sister is dead, in order that she may enter his house.
3) A man also is not believed when he states my brother is dead, so that he may have yibbum with his wife, nor [when he states that] his wife is dead, in order that he may marry her sister.
Section one: As we stated in the previous two mishnayoth, a woman is believed if she make a statement which does not change the status quo established when she left to travel abroad. If when she left she did not have a brother-in-law, and then she returns and states that her husband had a brother, but he died (in this case it doesnt matter whether her husband died first or his brother) she is allowed to remarry without yibbum. After all, if she hadnt stated that she had a brother-in-law, we would never have thought to make her wait until she had halitzah or yibbum to remarry.
Section two: In this case, the status quo when she left is that she had a brother-in-law. The mishnah teaches that a woman is never believed to state that her brother-in-law died. A woman is only believed to state that her husband died. The reason is that we assume a woman will make sure her husband is dead before she remarries. There is an assumption that she will not lie. Furthermore, if she was lying and he returns, the consequences for her are serious. However, there is no such assumption that a woman will not lie concerning her brother-in-law.
She is also not believed to state that her sister died, so that she could marry her sisters husband. Since even if her sister was alive, she would not cause serious consequences to herself by having relations with her sisters husband, she might lie.
We can see here a general pattern emerging: a person is less likely to lie if there are serious consequences awaiting him/her if he does lie. Therefore, in these types of situations, s/he is believed.
Section three: Finally, a man is not believed to state that his brother has died, so that he might marry his brothers wife, for the same reason we wrote above. Since there are no serious consequences for him if he is lying (and only serious consequences for her) he is not deemed trustworthy. So too a man is not believed to state that his wife has died in order to marry her sister for even if he was lying there are no serious consequences for him