Mishnah nine deals with a married woman who was taken captive or held in prison by non-Jews. The question under discussion is whether we must be concerned that she had relations with a non-Jew, whether by force or willingly, and how this affects her permissibility to her husband.
The two situations in the Mishnah:
She was taken captive or imprisoned over a monetary matter - for example, they held her in order to extract money from her family, or as security for a debt owed to them. In any case where the matter is monetary, she is permitted to her husband, even if he is a kohen. That is, we assume that she was not violated at all, since had she been violated by force she would have been forbidden to her husband the kohen, while to a husband who is a Yisrael she would have remained permitted.
She was taken captive over a matter of life and death - where they threatened to kill her and her life was in danger, she is forbidden to her husband, and according to one opinion even if he is a Yisrael.
The reason for the distinction between money and life:
The Gemara explains that when the matter is monetary, the non-Jews are afraid of losing the financial benefit if they take advantage of her, and because of that they are more careful with her. Therefore we may assume that she was not violated. But when they are about to kill her, they have no such concern at all.
The Gemara adds a qualification: this leniency in a monetary matter was stated specifically where the hand of Israel is strong and they hold sway over the non-Jews. But when the hand of the non-Jews is strong, we are concerned that they may have had relations with her even in a monetary matter. This concern is a concern of force alone, and therefore it is sufficient to forbid her only to a husband who is a kohen.
Does the prohibition in a matter of life and death include the wife of a Yisrael as well?
One opinion among the commentators: the Mishnah forbids her even to a husband who is a Yisrael. The reason: the wife of a Yisrael becomes forbidden only if she had relations willingly, and in a situation where they are about to kill her we are concerned that she may have had relations with him willingly in order to save her life, and in those circumstances she is forbidden even to her husband who is a Yisrael.
A second opinion: the entire Mishnah deals exclusively with the wife of a kohen, and only regarding her does the concern exist. The wife of a Yisrael would not have had relations willingly even where her life was at stake, and the only concern is that she may have been forced - a concern that applies to the wife of a kohen alone.
"Ir shekevashah karkom":
A city that was placed under siege and the siege succeeded in capturing it, and the non-Jewish enemy entered it - "kol kohanos shenimtze'u besochah" - every wife of a kohen who was found in that city is forbidden to her husband like any captive woman, because of the concern that they may have been forced by the soldiers.
"Im yesh lah edim afilu eved afilu shifchah - harei elu ne'emanim" - a single witness suffices, even a slave or a maidservant, to testify that they know she was not forced, and they are believed in their testimony.
"Ein adam ne'eman al atzmo" - the woman herself cannot testify about herself, and likewise her husband cannot testify on her behalf. They are not believed, because they are considered relatives of themselves.
The Mishnah continues and brings the words of Rabbi Shimon ben Katza, who was a kohen, and who swore by the sanctity of the Beis HaMikdash: "HaMa'on hazeh" ('HaMa'on' is a designation for the Beis HaMikdash), "lo zazah yadah mitoch yadi mesha'ah shenichnesu sonim liYerushalayim ad sheyatzu" - that is, his wife's hand did not leave his hand from the moment the conquerors entered Jerusalem until they left, and he testifies that he held on to her the entire time and knows that nothing happened. They said to him: a person is not believed about himself, and his testimony is not accepted.
A single hiding place that saves them all:
The Gemara adds that even in a city that was captured, if there was one hiding place in it, that is enough to permit all the women to their husbands who are kohanim, even though the hiding place holds only one person.
The reason for this is the principle of migo: every woman could have claimed "I was in that hiding place." And since she could have said so, she is believed in her present claim as well: "I know that I was not forced and did not come into contact with any man, and therefore I am pure." Her claim is accepted by virtue of the stronger claim she could have made. Therefore every woman, even one who admits that she was not in the hiding place, is believed when she says that she had no contact, and she is permitted to her husband the kohen.
In summary: in this Mishnah we learned the law of a woman who was taken captive or imprisoned by non-Jews: in a monetary matter she is permitted even to her husband the kohen, and in a matter of life and death she is forbidden - and the commentators disagree as to whether the prohibition applies even to the wife of a Yisrael, out of concern that she had relations willingly to save her life, or whether the entire Mishnah refers to the wife of a kohen and to a concern of force alone. We also learned the law of a city captured by siege, the credibility of a single witness even a slave or a maidservant, the rule that "a person is not believed about himself" as emerges from the incident of Rabbi Shimon ben Katza, and the power of a single hiding place to permit all the women of the city through the principle of migo.