לע"נ ר' אלכסנדר זושא ב"ר יוסף ז"ל
Says the Rambam [She-ar Avos Ha-Tumah - a favorite of so many people (good to know if you are ever asked to give a shiur and need a topic) - 1-5]:
חלב בהמה טהורה שמתה טהור שנאמר וחלב נבילה וחלב טריפה יעשה לכל מלאכה ואכול לא תאכלוהו מי שאיסורו משום נבילה וטרפה ואם הוכשר במשקין המכשירין הרי הוא כאוכלין טמאין ואינו כבשר נבילה והנוגע בחלב החופה את הכוליא קודם הפרשה הרי זה טמא כנוגע בכוליא עצמה שהרי כמה חוטין נמשכין ממנה בחלב אבל בהמה טמאה והחיה בין טהורה בין טמאה אחד בשרה ואחד חלבה לטומאה ומטמא אדם וכלים בכזית כבשר הנבילה:
The fat of a kosher animal that died without ritual slaughter is ritually pure, as implied by Vayikra 7:24: "The fat of a domesticated animal that died or the fat of a domesticated animal that was torn to death may be used for any purpose." The license granted by this verse applies to an entity forbidden only because the animal had died or was torn to death. If such fat was made fit to contract impurity due to contact with liquids that convey that status, it is considered as impure food and not as the meat of a dead animal.
Nevertheless, when one touches the fat the surrounds the kidney of a kosher domesticated animal that died without ritual slaughter before it was separated from the kidney, he is impure like one who touches the kidney itself. The rationale is that several strands of flesh from the kidney itself extend into the fat.
With regard to a non-kosher domesticated animal and a wild animal, whether kosher or non-kosher, the same laws apply to both its meat and its fat with regard to ritual impurity. An olive-sized portion imparts impurity to a person and to keilim like the meat of a dead animal.
A] The reason that חלב בהמה טהורה שמתה is טהור Is because the חלב doesn't have the status of בשר which is Tamei [ראב"ד תורת כהנים צו פרשה י' ה"ה]. Now this is only with respect to דיני טומאה but when it comes to all other halachos it has the status of בשר.
B] This also includes the חלב of a שור הנסקל and an עגלה ערופה that are אסור בהנאה but are still not מטמא, as the Gemara [Zevachim 70b] teaches. Why did the Rambam omit this halacha of the Gemara??
C] When an animal that gave birth to a stillborn, there is a מחלוקת whether the חלב is טמא or טהור. The Magid Mishna says that it is a ספק according to the Rambam. If so, says the Minchas Chinuch [147], if תרומה comes into contact with such חלב, it would not be burned [because maybe it is טהור]. Nor is there a חיוב of ביאת מקדש after coming into contact with this חלב.
D] Says the Maharam Chalava [Pesachim 23a]:
D] Says the Maharam Chalava [Pesachim 23a]:
"אלא שאני תמה היאך אפשר שיהא חלב נבלה טהור דאפילו תמצא לומר דאין החלב בכלל נבלה, מ"מ הא קא נגע בה, ומי עדיף חלב מאדם הנוגע בנבלה שהוא טמא וכו' אלא נראה דלכו"ע חלב נבלה טמא הוא אלא הכא בחלב טריפה הוא דפליגי וכו' עכ"ל.
Maybe חלב of a נבילה isn't טמא as a נבילה but it came into contact with a נבילה and should be at least a ראשון לטומאה!
One contemporary Rosh Yeshiva asked how it can become Tamei by contact when it lacks מחשבה - the requisite thought to render it food. But this is not a question according to the Rambam who is explicit in Tumas Ochlin 3-3 that חלב doesn't require מחשבה.
What is difficult on the Maharam Chalava [as noted by numerous people] is that in order to be מקבל טומאה it needs הכשר - i.e. water to fall on it and that is lacking here.