Yevamos - Believability of A Single Witness That Her Husband Died

There is a major machlokes Rishonim based on the gemara on 88a which implies that the right to belive an eid echad that a woman's husband died, is only d'rabonon. The Pischei Teshuva 17:13 cites the Nimukei Yosef who maintains that the eid echad is believed m'doraysa, since the eid echad is complimented by the fact that she will be dayak u'minsiba, meaning she will be cautious not to remarry until she properly researches that her husband is dead. This assumption creates a chazaka that if she remarries the husband is dead even from a d'oraysa perspective. But, Tosafos and other Rishonim maintain that it was a special leniency instituted by the Rabonon, and Tosafos pushes to explain why it would not qualify as uprooting a Torah law, since that is really what is happening for the sake of trying to be lenient to be matir an Agunah.

One way or the other, the beleivability of a woman is based on the assumption that she will be cautious before remarrying to properly research and make sure that he is dead.

R' Akiva Eiger discusses in a Teshuva (123) a situation where a woman got remarried without any testimony, she had children from the second marriage, and only after she died did an eid echad show up to testify that her first husband died prior to her remarriage so that these children from the second marriage are not mamzeirim. R' Akiva Eiger is not sure whether the eid echad is sufficient since the chazaka of dayaka uminsiba, that she will be cautious to research, only applies if she is working of the testimony of an eid, but in this case we may have to assume that she remarried without any research so the eid echad is not believed and her children are mamzeirim (In the end he seems to rule leniently).

Another question that he raises is in a case where a woman's husband disappeared and she committed adultery, then a single witness came and said that after she committed adultery (and became forbidden to her husband) her husband died. Do we rely on the eid echad in conjunction with the fact that she will be dayaka, because normally she is dayaka to prevent becoming assur to her first husband, but here she will anyway be assur to her first husband because of adultery, but maybe she will be dayka to prevent her from being assur to her second husband or to prevent her children from becoming mamzeirim?