One who brings a divorce document who must say: "In front of me it was written and in front of me it was signed," and likewise a single witness who testified for a woman that her husband died, may not marry her because of suspicion [that he lied in order to marry her]; but if he married her, he need not divorce her. But one who brings a divorce document who needn't say: "In front of me it was written and in front of me it was signed" [i.e. he is just the messenger and not a witness to its writing or signing] is permitted to marry her, since she is not [eligible to] marry based on his word. And two witnesses who testify for a woman that her husband died, it is permitted for one of them to marry her, since two people don't ordinarily sin for the sake of one [of them]. And see this in this Tur [Even haEzer] 141. Rem"a: In the responsum of the Ro"sh that he brought in Even haEzer. And there are those who say that even with two [witnesses testifying about the death of her husband], although it is permitted [for one of them to marry her], in any case a pious person will distance himself from this. (Hagahot Maimoni ch. 10 of Gerushin, Kol Bo, and Tosafot on Yevamot.)
A woman who vowed not to receive any benefit from her husband, and he did not annul [that vow] for her, and she came before a Sage to release her [from the vow], and he forbade her [and as a consequence she and her husband must divorce] because he did not find for her an opening to release her, [the Sage] may not marry her, lest they say: "He forbade her in order to marry her." But if he married her, he need not divorce her. This applies to an individual expert, but a court [of three] is not suspected [of not releasing her from her vow so that one of them could marry her]. Based on this reason, if [a young girl] refuses [to marry a man whom her mother or brothers arrange for her to marry when she was a child] or is released from a levirate marriage in front of a court, one of them [= the members of the court] can marry her.
And all of them who are married to others, and become widowed or divorced, are permitted to be married to them.
And any of them who had wives at that time [that they testified about the death of a woman's husband or her divorce document], and afterwards their wives die or they divorce them, and it was the women who convinced their husbands to divorce them, they may marry [the woman about whom they testified] ab initio. Rem"a: If their wives were sick [at the time they testified] and die [after their testimony] they may not marry [the woman about whom they testified]. (Nimmukei Yosef ch. 2 of Yevamot) And every one of them is permitted to marry the son of the witness who testified for her or the son of the Sage who forbade her to her husband, or any other relatives [of the testifier or Sage], for none suspect that they removed them from their husbands for the sake of their relatives.