Challah, Chapter 1, Mishnah 8. This mishnah deals with what is called 'dough of dogs' - dough made from a mixture of flour and bran, usually prepared as food for dogs, since the bran makes it coarse. But there are different grades of such a mixture, and depending on the ratio of bran to flour, it may or may not be fit for a person to eat in the ordinary way. Many halachic differences flow from this distinction, and our mishnah will teach us about them both in the laws of challah and in many other areas of halachah.
"Isas hakelavim, bizman sheharo'im ochlin mimenah":
The shepherds are the ones who employ the dogs to guard their flocks. When the mixture is such that even the shepherds themselves eat from it, the dough is considered real dough and real bread in every respect, and the following laws apply to it:
"Chayeves bechallah" - it is full-fledged bread, and therefore the obligation to separate challah applies to it.
"Ume'arvin bah" - it may be used for eruv techumin, by which a person extends his Shabbos boundary by placing bread at a certain spot; and also for eruv chatzeros, by which the residents of different houses that open onto a shared courtyard take joint ownership in a loaf of bread, and this loaf joins them together and permits them to carry in the courtyard on Shabbos.
"Umishtatfin bah" - it may likewise be used for shitufei mevo'os. The courtyards opened onto an alleyway called a mavoi, and each mavoi had several courtyards; in order to permit carrying in the mavoi, a shituf mevo'os was needed, which is also made with bread, and it is essentially an eruv chatzeros on a larger scale.
"Umevarchin aleha" - one recites the berachah of Hamotzi over it, as well as Birkas Hamazon.
"Umezamnin aleha" - one joins together for a zimun, saying "Rabosai nevarech".
"Vene'efeis beyom tov" - it may be baked on Yom Tov, since it is destined to be eaten by people as well. One may not bake or cook on Yom Tov for a dog or for any animal, but one may do so for a person, and this dough is fit for human consumption.
"Veyotzei bah adam yedei chovaso baPesach" - a person fulfills his obligation of eating matzah with it.
The shepherds do not eat from it:
If, however, the mixture contains so much bran that the shepherds do not eat from it and it is not fit for human consumption, then it is exempt from challah, one may not use it for an eruv or for a shituf, one does not recite Hamotzi or Birkas Hamazon over it and does not make a zimun over it, one may not bake it on Yom Tov, since it is fit only for animals and one does not cook for animals on Yom Tov, and a person does not fulfill his obligation of matzah with it on Pesach.
"Uvein kach uvein kach metam'ah tumas ochlin":
Finally, the mishnah teaches that even when the shepherds do not eat from it and it is not fit for human consumption, with regard to the tumah of foods it has the status of food in every respect and is susceptible to tumah - even though it is essentially meant for animal feed. The reason: since in a pinch people are able to eat from it, it is still included in the category of food that becomes tamei. The limit is until it becomes unfit even for a dog to eat, so that not even a dog would eat from it.
In summary: In this mishnah we learned that the halachic status of dough of dogs is determined by the extent to which it is fit for human consumption. When the shepherds eat from it, it is obligated in challah, one may use it for an eruv and a shituf, one recites a berachah and makes a zimun over it, it may be baked on Yom Tov, and one fulfills the obligation of matzah with it. When the shepherds do not eat from it, all these laws no longer apply. And either way, with regard to the tumah of foods it has the status of food, until it becomes unfit even for a dog to eat.