Eruvin, Chapter 6, Mishnah 7. This mishnah deals with relatives who live together: at what point are they considered one household, and when are they considered separate households?
The words of the Mishnah:
The mishnah speaks of "achim she'hem shutafin" - brothers who are partners. Some texts do not have the word "shutafin" here, since this definition is really relevant only when they are brothers. The case is brothers "she'ochlin al shulchan avihen" - who eat at their father's table, but each one sleeps in his own private house. In such a case, each and every one of them must join in the eruv separately, since they sleep in separate houses.
Understanding the expression "eating at their father's table":
The Gemara clarifies that this does not mean that they literally eat at their father's table, but rather that they receive their food from their father - from his table and his kitchen - and eat it in their own separate houses. It turns out that both the sleeping and the eating take place in separate houses, and therefore they are considered separate, and each one of them is obligated to join in the eruv of the courtyard that they are part of.
Therefore, if one of them forgot and did not join in the eruv, he must perform bittul reshus, nullification of his domain, so that they will be able to carry.
When is each of the brothers required to join in the eruv?
When the eruv of the courtyard is brought and placed in another house, one that is not theirs and not their father's house - the house in which they have a certain partnership.
Two cases in which they do not need to make an eruv:
The eruv comes to them - when the eruv is placed in their father's house. The halachah is that the person in whose house the eruv is placed does not need to add food of his own to the eruv, and he is included in it automatically.
There are no other residents with them in the courtyard - when there is no one in the courtyard besides them.
In both of these cases they do not need to join in the eruv, since for this purpose we view them all as members of their father's household.
In summary: Brothers who receive their food from their father's table but sleep and eat in their own private houses are considered separate residents, and each one of them is obligated to join in the eruv of the courtyard; and if one of them forgot and did not make an eruv, he nullifies his domain. This applies specifically when the eruv is brought and placed in another house. But if the eruv is placed in their father's house, or there are no other residents with them in the courtyard, they are all considered members of the father's household and do not need to make an eruv.