In this Mishnah, we're going to talk about a situation where two people died and we don't know who died first. Let's say a building fell on two people, and we're unsure who died first in the collapse. That creates a safek (uncertainty) in terms of the laws of inheritance. We'll spell it out as we read the Mishnah.
The Mishnah says: “If a house fell upon a person and his father”—let's call that person the son—“or a house fell on a person and also somebody who would give him an inheritance.” For example, there could have been a situation where his brother would have been giving him an inheritance. But we'll focus on the first case. It's really the same din (law), but the first case will make it easier.
A man and his father. A man named Reuven. They both died when a house fell upon them. Now we know they're both dead, but we don't know which one died first. Reuven also had an obligation to pay a ketubah (marriage contract) and another creditor, somebody he owed money to. But the problem was that Reuven died without any money whatsoever. His estate was penniless when he died, so he couldn't take care of these obligations. But his father, who also passed away, had money. His estate did contain property. So the question becomes: Who died first? If the father died first, then Reuven automatically inherited from him at that moment. So Reuven died with some money owed to him. The creditors and his wife, who was owed a ketubah, could collect from the father's inheritance because Reuven inherited it. But if Reuven died first, then his father died, Reuven died penniless, and he wasn't alive to inherit at that time. Therefore, his creditor and his wife wouldn't be able to collect the ketubah, because Reuven wasn't alive to inherit. So that's how this Mishnah will play out.
Yorshei ha'av omrim: The heirs of the father—that means the brothers of Reuven, who are collecting their inheritance—are trying to say, “It's possible that Reuven died first, and then our father died afterward. So the father's property never entered the possession of Reuven, the son. The wife and the creditors would have no claim on that money, but the regular inheritors would receive their father's money.” But the creditors and the wife are saying, “No, the father died first, and then Reuven, the son, died afterward. Once the father died, the property entered the domain of Reuven, and therefore the creditors, the people trying to collect the debt, have the right to take it from the inheritance, because what they're owed is now technically within Reuven's ownership, and he then died.” So what do we do in this case, where we don't have the ability to clarify?
Beit Shammai omrim yechaloku: the opinion of Beit Shammai is that they divide the property. Since it's not known which of the relatives died first, we say that both of these claims have an equal claim to the property. So the creditor collects half of what he's owed, and the other half goes to the brothers, who keep it as part of their inheritance. That's the opinion of Beit Shammai.
And Beit Hillel omrim: the property remains in its presumed status. The presumed status of this property is that it started off belonging to the father, and then we assume that when he died, it would go to his inheritors, to his heirs. So we view the property as if it's already in the possession of the father's heirs. The people trying to claim that they're entitled to collect some of the property have to first prove that the father died first. They have to establish that the father died first and then Reuven automatically became involved in that inheritance, so they can take it from Reuven. If they can't prove that, then the property is awarded to the father's inheritors.
We basically say that since they're bound to collect from him, it's as if they already had the money. And they have a chazakah—they're holding onto the money—and it's up to the people trying to remove it from them to bring proof. Therefore, the wife in this case and the people who were owed money get nothing according to the opinion of Beit Hillel, and the other brothers, who are the inheritors of their father, would get the rest of the property.

