Nazir, Chapter 6, Mishnah 11. The Mishnah deals with a nazir who has completed the days of his nezirus and has begun bringing his offerings: "Mi shenizrak alav echad min hadamim" - he brought one of the offerings and its blood was sprinkled, and at that very point he became tamei. The question is what his status is: once the blood of one of the offerings has been sprinkled on his behalf, is the tumah considered a tumah that occurred after the nezirus, or is he still in the midst of his nezirus?
The view of Rabbi Eliezer - "soseres hakol":
Rabbi Eliezer says: "soseres hakol" - it cancels everything. That is, all the offerings he brought, even those brought before he became tamei, do not count for him, and he must wait seven days, purify himself from his tumah, and only then bring the rest of his offerings.
It should be emphasized that Rabbi Eliezer does not mean that he must count all the days of nezirus over again, since he is at the end of his nezirus. His point is that the offerings he brought are invalid, because he became tamei before he completed all of the offerings. Rabbi Eliezer holds that a person does not become permitted to drink wine, and his nezirus does not fully end, until he has performed all the required acts and brought all the offerings. And since he became tamei before all the offerings were brought, even those brought before the tumah are void, and he must bring them again.
The view of the Chachamim:
The Chachamim disagree and say: "yavi she'ar korbenosav v'yitaher" - he brings the rest of his offerings and becomes tahor. The wording is phrased in reverse order, but in practice he must first purify himself, and afterward bring the remaining offerings that he had not yet brought up to that point. The offerings he brought before becoming tamei are valid and present no problem at all.
The basis of their view: once a person has successfully brought one of the offerings and its blood was sprinkled, he is considered to have completed his nezirus and is permitted to drink wine. True, he cannot bring the remaining offerings while he is tamei, and therefore he must purify himself; but once he is tahor, he brings all the offerings he has not yet brought, and every offering he brought earlier remains valid.
The incident with Miriam of Tadmor:
"Amru lo" - the Chachamim cited to Rabbi Eliezer an actual incident to support their position: "Ma'aseh b'Miriam haTarmudis shenizrak aleha echad min hadamim" - this woman had completed her nezirus, and one of the nezirus offerings had already been brought and its blood sprinkled. "Uva'u v'amru lah al bitah shehi mesukenes" - they came and told her that her daughter was in mortal danger. "V'halchah umatz'ah osah shemesah" - she went and found that she had died, and as a result she became temei'ah.
"V'amru chachamim" - and the Chachamim ruled in that case that since she had already successfully brought one offering, "tavi she'ar korbenoseha v'siaher": after she undergoes the process of purification and becomes tehorah, she may bring the rest of the offerings. And the offering she brought before becoming temei'ah still counts for her, since according to the Chachamim she had in effect already completed her nezirus.
In summary: in this Mishnah, Rabbi Eliezer and the Chachamim disagree about a nazir who became tamei after the blood of one of his offerings was sprinkled. According to Rabbi Eliezer, as long as all the offerings have not been brought the nezirus has not ended, and therefore the tumah "cancels everything" and he must bring his offerings anew after his purification. According to the Chachamim, the sprinkling of the blood of one offering ends the nezirus and permits him to drink wine, and therefore the earlier offerings are valid, and after his purification he brings only the remaining offerings - and so they also ruled in practice in the case of Miriam of Tadmor.