In memory of my great-great grandfather, Harav Yosef Michel Newberger, whose 75th yahrzeit was on Friday.
This is related to a point discussed in the Noda Biyehuda: this man should not have married the daughter of the woman with whom he had an affair, but it's midirabanan so now that he is married and has not repeated the aveira he may remain married to his wife.
I was looking at the gemara related to this din - Yevamos 97a: The mishna says if someone seduced or raped a woman he is allowed to marry her mother, sister or daughter, and it is not a prohibition of isha u'bitah or isha v'achosa. Then the gemara asks a contradiction: one who was leaning from a woman "hanitan min ha'isha"is forbidden with her mother, her daughter and her sister midiraban. How can our mishna say he's allowed to marry her close relative? (Note: hanitan implies they were not married but had a relationship.) The gemara answers he may marry her sister, mother or daughter after she dies. But while she is alive he may not.
The Rambam (Issurei Biah 2:11) paskens this gemara on 97 a bit strangely: One who had illicit relations, her seven relatives do not become prohibited to him. But the chachamim forbade one who committed adultery with a woman, to marry any of her 7 relatives as long as the woman (zonah) is alive. Because the woman (zonah) will visit her relative and he will be alone with her and his heart will desire her and they will come to an aveira. And moreso, even if he was leaning on a woman (nitan al ha'isha) he should not marry one of her relatives until she - the one he leaned on - dies. If he married the relative he does not have to divorce her. Why dies the Rambam list the cases separately? Maybe because the first case is where we knew there was a relationship and the second case is where it's only rumored. Or, the first case is an illicit relationship - maybe with a married woman, and the second case is where it was a permitted relationship (kiddushin would be tofsin) but it was outside of marriage.
I recalled the mishna in Yevamos 24b: one leaning on a servant "nitan al hashifcha" and she was freed; or on a non-Jewish woman and she converted, ho should not marry her, but if he did, he does not have to diverce her. One who leaned on a married woman "hanitan al eishes ish" and her husband sent her away [i.e., divorced her] even though they got married, he must divorce her. Why does 97a say min ha'isha and on 24 it says al hashifcha etc.? I think that on 97 the relationship ended. Still it's asur to marry her relative until she dies. On 24 it's a case where the relationship is ongoing. In fact, Rav Moshe Feinstein in Igros Moshe E"H 27 quotes himself in Dibros Moshe Yevamos (I think it's page 312 - hearos Yevamos perek 2 os 52) that the problem in the cases on daf 24 was that these relationships were rumors, and the subsequent marriage gives validity to the rumors. But where it's known, and it's not a rumor, it is not prohibited to marry the freed shifcha or convert.
Famous Teshuvas Harambam 132 in Pe'er Hador about this nitan al hashifcha; he's matir not because it's really mutar, but because of Takanas Hashavim.
Teshuvos Rabi Akiva Eiger 121 (in Even Haezer) discisses a shaila where a woman claims to have converted with her daughter. The validity of the conversion was in question because it was from a faraway place and was never confirmed; she married a man, there were rumors he was playing around with the daughter, and after the mother died he went around until he found a rav who would marry them (he omitted some details and when that Rav found out all the details he was very upset about it). So he discusses both these issues - the nitan al ha'isha and also isha u'bita in an unusual circumstance.
As always, see those teshuvos inside for the context and exact circumstances discussed.