Yevamos, Chapter 2, Mishnah 1. In the first chapter, in the first mishnah, the list of fifteen forbidden relatives included "the wife of his brother who was not in his lifetime." The underlying principle is as follows:
A brother's wife is by default forbidden as an ervah.
The only permission ever granted regarding a brother's wife is the mitzvah of yibum.
If the yavam, the surviving brother, was never alive in the world at the same time as the brother who died - not even for a single moment - the mitzvah of yibum does not apply to him at all.
Since there is no yibum, the widow remains in the category of an ervah, and therefore her co-wife too is exempt from both yibum and chalitzah according to Beis Hillel.
"Keitzad eishes achiv shelo hayah be'olamo?":
The mishnah sets out to clarify how such a case comes about, and describes the sequence of events:
"Shenei achim u'meis echad mehem" - there were two brothers, and one of them died.
"Ve'nolad lahem ach" - after his death a third brother was born, who was never alive during the lifetime of the deceased.
"Ve'achar kach yibem hasheni es eishes achiv u'meis" - the second brother, who was alive in the lifetime of the deceased, performed yibum with the widow who was bound to him, and afterward he too died.
The result is that the second brother had two wives: his original wife, and the widow he had married through yibum. In relation to the third brother, that yevamah is the wife of his brother who was not in his lifetime, since he was not alive in the days of the first brother, and therefore she is forbidden to him as an ervah. From here the mishnah rules:
"Ha'rishonah yotzeis mishum eishes achiv shelo hayah be'olamo" - the wife of the first brother goes free without yibum and without chalitzah, because she is an ervah with respect to the third brother.
"Ve'hasheniyah mishum tzaratah" - the original wife of the second brother also goes free, under the law of the co-wife of an ervah.
"Asah bah ma'amar":
The mishnah now discusses a case in which the second brother did not actually perform yibum, but only made a ma'amar with her. A ma'amar is a rabbinic form of betrothal that the Sages instituted as a preliminary to yibum: by Torah law the marital act itself constitutes the mitzvah of yibum, but the Sages instituted that he should not come to her without a prior ceremony. However, this betrothal is rabbinic only, and it does not accomplish the Torah's mitzvah of yibum.
Therefore, when the second brother made a ma'amar with her and died, the widow herself is an ervah to the younger brother, as the wife of his brother who was not in his lifetime. The question concerns the co-wife - the original wife of the second brother. In truth she is not the co-wife of an ervah by Torah law, since the ma'amar alone did not make the two of them co-wives to one another, and yibum was never actually performed.
By Torah law, then, the second woman is obligated in either yibum or chalitzah. The problem is that we cannot permit her to undergo yibum, because she has the appearance of being the co-wife of an ervah on account of the ma'amar. That is why we learned: "Choletzes ve'lo misyabemes" - she performs chalitzah, since by Torah law she requires either yibum or chalitzah; and she does not undergo yibum, because of the appearance of being the co-wife of an ervah.
In summary: In this mishnah we learned how a case of "the wife of his brother who was not in his lifetime" comes about - when the younger brother was born after the death of the first brother, and the middle brother performed yibum with his widow and died. In such a case both women go free: the first because she is an ervah, and the second because she is her co-wife. But when no yibum was performed and only a ma'amar was made, there is no Torah-level status of co-wife of an ervah, and therefore the second woman performs chalitzah and does not undergo yibum.