In Masechet (tractate) Bava Batra, Perek (chapter) Tet (nine), Mishnah Yod (ten) is the last Mishnah in the Perek. It discusses an accident involving two relatives. Here, we'll talk about an accident involving a man and his father, who both die, but we don't know which one dies first. The mother was unmarried at the time, and the son she had was her only child.
If the mother died first and then her son, her son would have inherited from her right away, for the brief moment that he was alive. Then his heirs would be entitled to whatever he owned, including his mother's possessions. If he died first and then his mother died, he would not have inherited from her. Her heirs would be her father or her siblings, and they would inherit the money at that point because they were next in line. So the question is what happens in this situation: did the mother die first, or did the son die first?
The Mishnah says, “A house falls on a person and his mother.” Both Beit Shammai and Beit Hillel agree that the heirs of both the mother here and her son—two separate people, with the heirs depending on how the family tree works out—divide the estate. In both of these cases, the sides have equal claims. Unlike the previous Mishnahs, where Beit Hillel and Beit Shammai argued about this, there was always a muchzak, somebody who was in possession, or someone we could assume was the rightful inheritor. But in this case, nobody has precedence. Each set of heirs is entitled to inherit the estate; neither one of them is the direct heir. Therefore, they are not considered to be the muchzak. They are both second-level heirs to the estate. So even in this case, Beit Hillel would agree that the estate is divided between the two of them.
Rebbe Akiva said he doesn't agree. He says that he agrees that in this case, too, there is a machloket (argument) between Beit Shammai and Beit Hillel about the property, and that it has a chazakah: a presumed status of belonging to the mother's heirs. The reason for that, according to Rebbe Akiva, is that when the mother was alive, her marriage had ended. As we were saying, she wasn't married at that point. She and her estate were in the chazakah. They were considered muchzak as belonging to the tribe of her father. A woman goes back to her father after she's divorced or after her husband dies. So her heirs have an advantage. Her son is dead along with her, so he is not an inheritor. Therefore, her father would inherit from her.
Just one quick note: we're also assuming that the son here did not have kids, because if he had kids, they would come in his stead. But we're assuming he possibly had half brothers in this case, from the same father but a different mother. So they wouldn't inherit from the same woman. A little bit complicated, but the entire son's line would be out. Therefore, the woman's father is considered to be a muchzak, because she belongs to that tribe. Her father is considered to be a muchzak, a person who could be possessive of that land. So Rebbe Akiva would say that even in this case, Beit Hillel would not divide the estate but would award all of it to the mother's heirs—possibly, just to make it easy, her father.
Amar lo Ben Azzai (Ben Azzai said to him). Ben Azzai answers Rebbe Akiva: “We're already arguing enough. We're already pained by the argument in the two previous Mishnahs. You're going to now make them argue on a case where they could finally agree. You're going to tell us that they're arguing on that case as well?” Ben Azzai disagrees with Rebbe Akiva. He says he agrees with the Tanna Kama (first Tanna). He would say that Beit Shammai and Beit Hillel don't argue in this case, and that both sets of heirs—the mother's heirs and the son's heirs—would divide this estate equally between them. According to Ben Azzai, the fact that the mother's father had a connection—a tribal connection—is not enough for him to be muchzak or for the mother's estate to go into the presumptive possession of her heirs. That's not how we work things. That's not how it works. That's not a real muchzak. Therefore, according to Ben Azzai, the Tanna Kama was correct, and there is no argument between Beit Shammai and Beit Hillel in this case.