Mishnah 6 in the first chapter of Tractate Bechoros comes to answer one question: from when does the redemption of a peter chamor take effect? Two possibilities stand before us:
The redemption takes effect immediately upon designating the lamb (or anything else with which one redeems the donkey), from the moment the owner says: this is the lamb with which I am redeeming.
The redemption does not take effect until that lamb is handed over to the kohen, and until then the donkey remains unredeemed.
Two models exist in halachah:
Maaser sheni: The produce that grows in the first, second, fourth, and fifth years of the Shemitah cycle, which must be brought up to Jerusalem and eaten there. One who does not want or is unable to bring it up redeems the sanctity of the produce onto coins and brings the coins up to Jerusalem. From the moment of redemption, the sanctity transfers to the coins and the food becomes completely mundane and may be eaten outside Jerusalem; and if the coins are lost by accident, the owner no longer has the responsibility to replace them.
Pidyon haben: The firstborn son is redeemed with five selaim - five silver coins. If a person designated five coins and said they are intended for the redemption of his son, and they were lost, he must bring five other coins, since the son is not redeemed until the coins actually reach the hands of the kohen. The mere designation and declaration are not sufficient.
It turns out that the question is: is the peter chamor redeemed already at the moment of designating the lamb, like the model of maaser sheni, or only at the time of actually giving it to the kohen, like the model of pidyon haben?
The source of the dispute in the verse:
The basis of the law is in the verse (Bamidbar 18:15): "Ach padah sifdeh es bechor ha'adam" - you shall surely redeem the firstborn Jewish son; and later in that same verse: "v'es bechor habehemah hatemeiah sifdeh" - also the firstborn of a non-kosher animal, and the intention is to a donkey, which is the only non-kosher animal that has redemption. It turns out that the verse draws a comparison between the laws of pidyon haben and the laws of redeeming a peter chamor.
Rabbi Eliezer: By virtue of the comparison, just as pidyon haben does not take effect until the money reaches the hands of the kohen, so too the redemption of a peter chamor does not take effect until the lamb is handed over to the kohen.
The Sages: The verse opens with the word "Ach", and every "ach" comes to exclude and limit the scope of the derivation. Therefore, there is a limit to what is learned from pidyon haben to the redemption of a peter chamor. Certain laws are indeed learned - for example, that the redemption of a peter chamor applies only when the owners are Yisrael, whereas a Levi or kohen who has a firstborn donkey in their possession is not obligated in redemption - but not all the laws transfer. And included in what is not learned is this: from the moment the owner designates the lamb and says "this is the redemption of my peter chamor", the redemption takes effect immediately.
The language of the Mishnah - if the lamb dies:
First, we will clarify the terms: "donkey" - the mother; "peter chamor" - the firstborn foal that was born; "the redemption of a peter chamor" - the lamb with which that foal is redeemed.
If a person separated a lamb for the redemption of the donkey that was born, and the lamb died:
Rabbi Eliezer: He is obligated to set up another lamb in its place. According to his approach, as long as the lamb has not reached the hands of the kohen, the donkey is not redeemed, exactly like the law of the five selaim of pidyon haben which must reach the kohen.
The Sages: There is no need to replace the lamb with another. If the lamb is lost after it was separated for redemption, the loss is the kohen's, just as with the redemption of maaser sheni produce, if the coins are lost there is no need to replace them in order to buy with them in Jerusalem.
The testimony of Rabbi Yehoshua and Rabbi Tzadok was given on that famous day when Rabbi Elazar ben Azaryah was appointed Nasi, as related in the Gemara in Tractate Berachos, and Rabban Gamliel was temporarily deposed - the day on which Tractate Eduyos was taught and various testimonies were delivered. Rabbi Yehoshua, the greatest of the generation, and Rabbi Tzadok, who was saved from Jerusalem through one of the three requests Rabban Yochanan ben Zakkai made, testified regarding the redemption of a firstborn donkey that died: "She'ein kan l'kohen klum" - there is no further obligation toward the kohen, and he is not entitled to a new lamb.
This does not mean that the dead lamb does not belong to the kohen: the carcass itself is the property of the kohen and must be given to him, and he may use it - to feed his dogs, to make glue from it, and the like - but nothing beyond that.
If the Firstborn Donkey Dies:
From here we move to the implication in the opposite case: "Meis peter chamor" - the young donkey died before the live lamb was handed over to the kohen. What is the halachah?
"Rabbi Eliezer omer: Yikaveir" - since the redemption of the firstborn donkey did not reach the kohen, the redemption did not take effect and the donkey remains unredeemed. Consequently, it is forbidden to derive any benefit from it, and nothing can be done with it other than burying it. "U'mutar b'hana'ato shel taleh" - the lamb that was set aside for the redemption, since it was never handed over to the kohen and the redemption did not take effect, remains in the possession of the donkey's owner without any lien, and he is not obligated to give the kohen anything.
The Sages: "Ein tzarich likaveir" - according to their view, from the moment the lamb was set aside, the firstborn donkey was immediately redeemed, and therefore it is permitted to derive benefit from the donkey's carcass and there is no need to bury it. "V'hataleh l'kohen" - the lamb that served as the redemption for the firstborn donkey belongs to the kohen, and it must be handed over to him.
In summary: Rabbi Eliezer and the Sages dispute whether the redemption of a firstborn donkey is derived from the redemption of a firstborn son, which does not take effect until the redemption reaches the kohen, or from ma'aser sheni, where the redemption takes effect immediately. The halachah follows the Sages: the redemption of a firstborn donkey takes effect the moment the lamb is set aside, and at that time the berachah over the redemption of the donkey is recited. Hence, if anything happens to the separated lamb - the loss is the kohen's.