The Mishnah (3:1) discusses meat sauce, thick bean soup or milk that congeals and liquifies. If they are liquid enough to make one's hand wet, then they are considered a liquid. Consequently, the decree regarding liquids would apply such that if they came into contact with any tumah they would be considered a rishon le'tumah. If they were tameh, and then congealed, the product would be considered a sheni le'tumah. The Bartunera explains that the hardened mass is considered food that has touched a rishon le'tumah liquid, which makes it a sheni le'tumah. If it subsequently liquifies, then it depends on the size of the mass before it begins to do so. If it were the size of a kebeitza, the minimum size for food to pass on tumah, the liquid would be tahor. The reason is that as soon as it begins to liquify, the mass will be less than a ke'beitzah, and unable to make the liquid tameh. It follows, that if the mass was larger than a kebeitzah then the liquid would be tameh.
The Mishnah Achrona notes that according to the simple reading of the Mishnah this is all one case. In other words, the milk became tameh, congealed and then became liquid again. The reason the liquid is tahor in the end, is because when it congealed it was no longer consider a liquid and the liquid in the end is considered new. This is the understanding of the Rosh.
The Rambam however understand the Mishnah is listing two separated cases. In other words, the second case is when the food became tameh when it was solid and after became liquid. If however it because tameh when it was liquid, then congealed and subsequently liquified, the liquid would return to its original tumah -- it would be a rishon le'tumah.
The Mishnah Achrona explains that the Tosefta appears to support this understanding. The case in the Tosefta is regarding tameh water that freezes and then melts. The water is tameh at the same level it was before it froze. The Mishnah Achrona however notes that the Rosh explains that that law only applies to water. The reason is that people do not generally eat ice as food. Therefore when it became ice, it was no longer water or food. Consequently, when it melts, it would return to its original status of tumah. Regarding the products in our Mishnah, since when they congealed, they became defined as food, the original status as water becomes null and void.
The Rash appears to maintain a middle position. He asks why when the mass liquifies does it became tahor? The tumah cannot just disappear. He suggests that when the Mishnah writes that it is tahor, it means that it tahor from the state it was as a liquid. Nevertheless, it is still a sheni le'tumah like the solid that preceded it.
The Divrei Yechezkel however asks that the question posed by the Rash applies to the first transition, from liquid to solid. One may ask, how did the tumah just disappear? How did it drop from a rishon to sheni? According to the above logic, the solid should still be considered a rishon. He suggests that in the first transition, when it became a solid, it lost its status as being a liquid. Consequently, had it encountered the tumah in this state it would have only been a sheni. That is why the first transition was not an issue. Once it is already food however, for food to lose its tumah it would need to spoil to a state that it would no longer be edible for a dog. It is for this reason why the Rash asks in the second transition only, how the tumah could simple disappear.1
1 The Divrei Yechezkel questions why, according to the Rash, the liquid should be considered a sheni le'tumah. Granted that the solid was not the size of a kebeitzah to make the liquid tameh, but why can the liquid that is sheni not make itself tameh? He leaves the question unresolved. Perhaps the answers is that the gezeirah that liquids that touch tumah are always treated as a rishon only applies when they came into contact with a source of tumah (and not one droplet with another). Recall that the gezeira was based on confusing liquids with liquids that came from a sheretz. Consequently, the gezeira would only apply to cases that mirror that case -- where it was in contact with a something that was tameh.
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