Gemara

(Beraisa - R. Shimon): Really, Minchas Chotei should require oil and frankincense, and a (standard) Chatas (e.g. for eating) Chelev should require Nesachim, so that a sinner not profit (save money). The Torah said that it does not, in order that his Korban will not be glorious.

Yevamos 92b (Shmuel): Due to our ignorance, (if a stranger was Mekadesh a Yevamah) she needs a Get (to marry anyone else).

Shmuel is unsure whether "Lo Sihyeh" teaches that this is a Lav, or that Kidushin does not take effect on her.

(Rav Ashi): According to this, if her Yavam is a Kohen (and Levi, a stranger, was Mekadesh her, they do Chalitzah, and she is permitted to Levi.

Objection: He should not profit (from his Kidushin, which was improper)!

Correction: Rather, if her Yavam is a Yisrael, Levi gives her a Get, and she is permitted to her Yavam.

Rishonim

The Rif and Rosh (Yevamos 29a and 10:3) bring the Gemara in Yevamos.

Rif (29b): Rav Yehudai Gaon says that if she married Levi (i.e. Nisu'in) without Chalitzah and had no children, she does Chalitzah is permanently forbidden to Levi and her Yavam (David). If she had children, if Levi is a Yisrael, David does Chalitzah and she stays with Levi. We do not make him divorce her, lest she look like a woman whose husband went away (and she remarried based on a false report of his death), in which case the children are Mamzerim. If he must divorce her, her children will be scorned (called Mamzerim). Some do not rely on this. If the Gemara held like this, it would have said so! The Yerushalmi concludes like R. Yochanan, who forces Levi to divorce her even if they had children.

Nimukei Yosef: R. Tam forbids her to Levi only b'Mezid, lest a sinner profit. The Ge'onim and the Ra'avad say that she accepted Kidushin b'Mezid. We conclude that she is permanently forbidden to the Mekadesh lest he profit, but she is permitted to her Yavam. It seems that the Rambam agrees.

Rambam (Hilchos Yibum 2:19): If a Yevamah became Mekudeshes to a stranger (Levi), she is not forbidden to her Yavam (David). Levi divorces her, and she does Yibum or Chalitzah. If David is a Kohen, who cannot marry a divorcee, Levi divorces her, so a sinner not profit, and her Yavam does Chalitzah.

Magid Mishneh: The Ge'onim forbid her to Levi even if David does Chalitzah willingly, lest a sinner profit. The Ramban disagrees. She should not be more stringent than a woman whose husband went away (and became Mekudeshes). She is permitted to her husband, and, if he divorces her, to the Mekadesh. Perhaps we are more stringent here, for she had no permission. Also the Rashba says that we forbid here, for she was Mezid.

Rambam (20): If Levi divorced her from Eirusin and had Nisu'in with her after Chalitzah, he need not divorce her. Had he made Nisu'in before Chalitzah, we would make him divorce her even if he remarried her after Chalitzah, for this is like a woman whose husband went away. She is forbidden to both men.

Rosh: R. Tam says that Levi must divorce her only if the Yavam (David, a Kohen) wanted to do Yibum. If David wanted to do Chalitzah, he does, and she is permitted to Levi. We do not fine one who was Mekadesh even regarding a woman whose husband went away! We are stringent (lest people say that she was divorced, married another and returns to her first husband) only when an Isur was done. She is forbidden to the latter only when she is forbidden to the first husband. All the more so we are not stringent about a Yavam, for even if she was Mezanah b'Mezid she is permitted to the Yavam. A case occurred in which a Yevamah did not know that she had a Yavam, and David was Mekadesh her. R. Tam permitted her to David after Chalitzah. We say 'he should not profit (from his Kidushin)', not to forbid her to Levi, rather, to teach that David need not do Chalitzah. We need not teach that she is permitted to Levi! If David wants to do Chalitzah, she is permitted to Levi. He did not profit through the Kidushin. If David does not want to do Chalitzah, she is an Agunah for life! When David is a Yisrael, the Chidush is that make Levi divorce her, lest he profit. However, if she had Nisu'in, even if David wants to do Chalitzah, she is forbidden to Levi.

Rosh (Sof Siman 3): BaHaG says that if she became Mekudeshes without Chalitzah, Levi divorces her and she is permitted to David. She is permanently forbidden to Levi, lest a sinner profit. If she had Nisu'in with Levi and he is a Yisrael, if she had children David does Chalitzah and she stays with Levi. We do not make him divorce her, lest she look like a woman whose husband went away, and her children will be scorned. R. Chananel disagrees. The Yerushalmi said that he divorces her, lest her children be scorned. It did not distinguish between whether or not she had children (already). In Gitin we say that if a Yevamah had Nisu'in without Chalitzah, all the fines (of one whose husband went away) apply. This is even if she has children. Presumably, R. Yirmeyah (in the Yerushalmi) permits her to stay only when she has children, and R. Yochanan forbids even in this case. R. Tam's opinion is primary. Even BaHaG forbids only lest a sinner profit, i.e. b'Mezid. Practically, if she had Nisu'in b'Shogeg, she leaves and all the fines apply. If Levi was Mekadesh her b'Mezid, she is forbidden to Levi, lest a sinner profit. If she thought that she has no Yavam, if her Yavam does Chalitzah she is permitted to Levi.

Poskim

Shulchan Aruch (EH 159:1): If a Yevamah became Mekudeshes to Levi b'Shogeg, he divorces her, and her Yavam (David) does Yibum or Chalitzah. If David was a Kohen, Levi divorces her, lest a sinner profit, and David does Chalitzah. If Levi had Nisu'in with her after Chalitzah, he need not divorce her.

Beis Yosef (DH u'Mah she'Chosav Rabeinu): The Tur holds that the Rambam permits Levi to keep her after Nisu'in even if his initial Kidushin was b'Mezid.

Gra (4): If Levi divorced her and remarried her after Chalitzah, he did not profit from his initial Kidushin.

Rema: Some say that even if he later had Nisu'in with her, we make him divorce her, because he was Mekadesh her b'Isur, i.e. they were Mezid. If they were Shogeg, i.e. they did not know that she has a Yavam, if David wants to do Yibum, Levi must divorce her. If David wants to do Chalitzah, she may have Nisu'in with Levi. Levi must Mekadesh her again after Chalitzah. This opinion is primary. Some say that this is only if they did not know that there is a Yavam. If a Yavam was here but she relied on hearsay that he died, she must leave Levi.

Beis Yosef (DH v'Chasuv): The Terumas ha'Deshen (222) says that even R. Tam would forbid if she became Mekudeshes because she heard that her Yavam died. I disagree. The Terumas ha'Deshen says that BaHaG forbids to the Mekadesh even if he made Nisu'in after Chalitzah, for we said that she is forbidden permanently. This is not necessarily correct.

Beis Shmuel (1): Most Poskim permit her to Levi in a case of Shogeg. The Mechaber forbids only when she heard rumors that her Yavam died. He would permit had she heard from a witness, for then she was truly Shogeg.

Beis Shmuel (5): If David is a Kohen, we do not force him to do Chalitzah, even if she was Shogeg. Only the Nimukei Yosef disagrees.