Ohalos, Chapter 11, Mishnah 6. This is very likely the briefest mishnah we meet anywhere in Maseches Ohalos, and yet it packs into a few words a full machlokes between Beis Shammai and Beis Hillel. The chapter has been dealing with a house whose doorway area, the miftan, stands at the border between inside and outside, and with what happens when a living person lies stretched out across that border, part of him on the threshold and part of him inside the house.
The Case
The setting is the same as the case that came just before it, with one crucial change. Earlier the tumah came from outside: two men carried a meis over the man who was lying there. Here the mishnah says "vetumah babayis", the tumah is inside the house itself. Once a source of tumah is in the house, the tumah fills the entire house as one ohel, and that includes the airspace under the part of the man's body that extends into the house, and, according to the way the question will develop, the space beneath him altogether.
Now people come along. They are not carrying a meis; they are simply passersby. They notice this man lying across the threshold and they lean over him, perhaps to ask whether he is all right and why he is lying in such a strange position. Whatever their reason, by bending over him they have formed an ohel above him. He himself is alive and well, so there is nothing wrong with what they are doing on the face of it.
The Question
The question is whether the tumah of the house travels underneath the man's body, and whether the narrow space beneath him then counts as an ohel of its own. If it does, then those people who bent over him were leaning over an ohel of tumah, and they become tamei.
Here we must keep in mind the principle that has been driving this whole discussion: a human body is not choitzetz bifnei hatumah. A person's flesh does not block tumah. So the man's own body offers no barrier at all; the only issue is how to define the space between his underside and the ground.
Beis Shammai: Tahor
"Beis Shammai metaharin." Beis Shammai rule that the people who bent over him remain tahor. They were not leaning over a meis at all. This man is alive; he is simply lying on the threshold, perhaps asleep. True, the interior of the house is a single ohel filled with tumah, but the part of him they leaned over is on the outer side. And shall we say that the tumah slips beneath him and that the space under him becomes an ohel in its own right, so that they were bending over that ohel? Beis Shammai say no. The space beneath him does not become an independent ohel, because the man is regarded as a single body, one guf, not as an upper structure with an airspace underneath it.
Beis Hillel: Tamei
"Uveis Hillel metam'in." Beis Hillel disagree. In their view the upper portion of the person is treated in halachah as a distinct entity. Once that is so, the gap between the underside of that upper portion and the ground beneath him, a space of a tefach, qualifies as an ohel. And since that ohel is continuous with the ohel of tumah inside the house, the tumah is present there as well. Mimeila, automatically, the people who leaned over the man were leaning over an ohel of tumah, and they are tamei.
The Underlying Point
Everything turns on that one halachah: a body does not block tumah. Were the man's flesh able to serve as a barrier, the people above him would have nothing to worry about, whatever the status of the space beneath him. Since it does not, the entire question comes down to whether we look at him as one solid guf, as Beis Shammai do, or as a covering with an airspace beneath it, as Beis Hillel do. If the space under him is an ohel, then everyone above him has a problem.