Sof Tum'a La-tzet
The mishna in Taharot describes a unique form of tum'at ohel. Generally, the halakha of tum'at ohel (as described in Parashat Chukat) determines that objects located under the same roof as a meit (dead body) acquire tum'a even in the absence of physical contact. The mishna, however, describes the halakha of "sof tum'a la-tzet," meaning, that an item located in the route that a meit will ultimately take when leaving a building also acquires tum'a. For example, if the meit will exit a door of the house and that door has an awning or canopy which extends above it, anyone or anything standing under that canopy receives tum'a – even if the meit has not yet traveled that route.
The simplest approach to understand this halakha is to somehow assume that even though the door through which the meit will travel is currently closed, we envision it as open. Rabenu Chananel in Masekhet Beitza (10a) claims that since the door will ultimately be opened, we can consider it already open based on the principle of "kol ha-omed." This principle allows certain future events to be considered as having already occurred. (For example, anything earmarked for burning is already considered burnt and cannot be mekabel tum'a; any blood earmarked for a korban is considered already sprinkled even though it hasn't actually been sprinkled, etc.) If we view the door as already open, we can then – through the conventional halakha of ohel - trace the 'spread' of tum'a through that 'open' door and under the awning, thereby conferring tum'a upon people or objects located underneath the awning. The Ra'avad, cited in the Shita Mekubezet to Bava Batra (13a), provides a slightly different variation when he claims that the tum'a 'breaks through' the closed door, thereby exiting and diffusing under the awning. This principle of "tum'a boka'at ve-yotze" is borrowed from several gemarot (see for example Chulin 126a), and dictates that certain forms of 'contained Tum'a' (generally Tum'a contained in a box without a tefach of airspace) breaks through and spreads upwards.
Conceivably, a very different understanding of sof tum'a la-tzet may be suggested. The aforementioned approach assumes that tum'at ohel in general is a product of the tum'a's spreading through the covered structure, thereby imparting tum'a to objects even without physical contact. If this is the mechanism of tum'at ohel, then sof tum'a la-tzet, a subsidiary of ohel, must operate by somehow opening the door, thereby allowing the tum'a to diffuse outside the house. We may, however, explain tum'at ohel along different lines. Although the tum'a does not spread, the halakha of ohel determines that any object within the same structure of a meit receives tum'a. Ohel does not operate through virtual contact, or contact without actual physical touching. Instead, ohel is a more formal or categorical phenomenon – any object in the precincts of the meit receives tum'a. If so, the halakha of sof tum'a la-tzet is merely an extension of the definition of these precincts. The basic halakha of ohel dictates that anything under one roof is deemed the precinct, whereas the extension of sof tum'a la-tzet envisions any ROUTE of the meit as its region. Sof tum'a la-tzet doesn't require the opening of closed doors, but rather stretches the definition of the 'area of the meit.'
The most vivid consequence of these approaches might be a situation where the route of a meit is physically distinct from the area of the meit. The case described by the mishna in Taharot concerns a route of the meit which is physically conjoined to the house (the exit route from the house presently containing the meit). Would the halakha apply to a doorway of another house or structure to where the meit will travel? If sof tum'a la-tzet entails the opening of doors and subsequent spread of tum'a, we might easily extend the halakha to these cases. Conversely, if sof tum'a determines a broader region of the meit (namely the route), it might only apply to areas which bear some architectural integrity to the actual site of the meit. A route of the meit which is distant from the current area of the meit (i.e. not physically conjoined) might not be deemed the area of the meit. The Shita Mekubezet in Masekhet Beitza cites an opinion denying the application of sof tum'a to areas which are not physically connected to the current house of the meit.
This question has interesting practical ramifications. The Rema in Yoreh De'ah 171 debates whether a kohen is allowed to pass by the gateway to a city in which a meit is located. Assuming the meit will depart the city through this gate, we might consider this a situation of sof tum'a la-tzet, thus, if the gate has a canopy or awning, anyone standing underneath it would acquire tum'a. Clearly, this gate is not architecturally integrated with the house of the meit. If sof tum'a la-tzet involves a definition of the broader area of the meit, we might not apply this definition to the gate of a city.
Another question impacted by the manner of understanding sof tum'a concerns the scenario portrayed by the mishna in Ohalot (8:6). Suppose a house contains three rooms and there is a half-zayit of a meit in each of the outer rooms which spill into the middle room (which doesn't contain any meit). Clearly, the middle room is tamei (namely, people standing there acquire tum'a). Since each half-zayit will ultimately enter the middle room, we can therefore 'envision' a full zayit present in the middle room. Should, however, the outer rooms be tamei? The mishna asserts that people standing in the outer rooms are tahor. If we adopt the simple approach to understanding sof tum'a la-tzet, this mishna is a bit startling. If we view closed doors as open, then all these rooms should be connected (by 'open' passageways) and the two half-zayits should be combined; anyone standing in ANY of these three rooms should then be tamei. If, however, sof tum'a establishes the environment of the meit, we might only consider the middle room to be its environment as it is only through this room that the meit will travel. Indeed, each outer room is an environment to a half-zayit of meit, but a half-zayit is insufficient to bestow tum'a. Only the middle room, as the ultimate route of the meit, can be considered a 'makom' of a zayit meit, and hence only objects in this room acquire tum'a.