The mishnah on today’s daf deals with a ringed urban living arrangement: an inner courtyard is engulfed by an outer courtyard, and both have several occupants. Only the outer courtyard has an opening to the street, so the people who live in the inner courtyard must always walk through it to get to the public sphere. Because this is their only exit, by dint of necessity the members of the inner courtyard have earned walking rights within the outer courtyard.
With regard to two courtyards, one of which was within the other, and the outer one opened into the public domain: if the inner courtyard established an eruv for itself and the outer one did not establish an eruv, carrying in the inner one is permitted and carrying in the outer one is prohibited.
Seems simple enough. If you and your immediate neighbors in the inner courtyard make an eruv, you can carry. Can the outer courtyard do the same?
If the outer courtyard established an eruv and the inner one did not, carrying in both is prohibited.
So members of the outer courtyard can make their own eruv, but if the inner courtyard doesn’t also have an eruv, it is invalid. Why? The people who live in the inner courtyard are members of both their own secluded cul de sac and of the larger outer courtyard. So an eruv in the outer courtyard is valid only if the people who live in the inner courtyard are also supported by an eruv.
An eruv only works if all the neighbors of a given space contribute to the joint food basket. If just one neighbor forgets to bring their contribution, it can render the eruv invalid. In this case, the mishnah conceives of this as two intertwined communities: the whole (both courtyards) and then just the inner courtyard — a community within a community.
The members of the larger, more inclusive community must operate with the public needs at heart; they have to take into consideration those who pass through even though they aren’t their most immediate neighbors. The members of the inner courtyard, on the other hand, have two distinct memberships. Once in a while, they may reap the benefits of their secluded membership in the inner courtyard and can operate independently from the larger public. But, they can’t simply split off from the larger world; with their dual membership, their actions impact both their inner sanctum and the larger community.