This is Mishnah 6 of the fifteenth chapter of Yevamos, which deals with the status of the rival wife in light of a woman's testimony that her husband has died - both regarding permission to remarry and regarding eating Terumah.
The words of the Mishnah:
"HaIshah shehalchah hi uva'alah limdinas hayam" - a woman who went overseas together with her husband, and returned alone, without her husband.
"Uva'ah v'amrah meis ba'ali" - she testifies and says that her husband has died.
"Tinasei v'sitol kesubasah" - she herself is believed: she is permitted to marry another man, and she collects her kesubah, as explained above.
"V'tzarasah asurah" - but her rival wife, the second wife of that same husband, is forbidden to marry, as explained above.
The status of the rival wife regarding Terumah:
"Haysah bas Yisrael l'kohen" - if the rival wife is the daughter of a Yisrael married to a kohen, so that by virtue of her marriage to her living husband she was eating Terumah, she continues to eat Terumah. The reason: since we have said that she is forbidden to remarry, we are treating her as one whose husband is presumed to be alive, and therefore she continues to eat Terumah. These are the words of Rabbi Tarfon.
Rabbi Akiva disagrees:
Rabbi Akiva says: "Ein zu derech motzi'asah midei aveirah" - this is not the way to remove the woman from the concern of transgressing a Torah prohibition. "Ad shet'hei asurah linasei va'asurah mile'echol biTerumah" - one must be stringent in both directions: not only is she forbidden to remarry, but she is also forbidden to eat Terumah, lest her husband did in fact die, and once he has died the daughter of a Yisrael no longer eats Terumah.
It emerges that according to Rabbi Akiva, we do not say that since we do not believe the rival wife that the husband died, she may take that leniently and relate to him as one who is certainly alive. We do not say this; rather, the doubt requires stringency in both directions. This is the position of Rabbi Akiva, who disagrees with Rabbi Tarfon.
In summary: in this Mishnah we learned that a woman who returned from overseas and said "my husband has died" is believed regarding herself - she may marry and collect her kesubah, while her rival wife is forbidden to marry. The Tannaim disagree about the status of the rival wife regarding Terumah: according to Rabbi Tarfon, since we have forbidden her to remarry, she is treated as one whose husband is alive and she eats Terumah; according to Rabbi Akiva, the doubt does not turn into a leniency, and therefore she is forbidden in both - in marrying and in eating Terumah.