Eruvin 70: Shabbat Status Quo

The case of 5 homes on a courtyard, where one forgot to join in the eruv, and he therefore renounces his rights to the courtyard, so that everyone else can carry - does he have to do so before each one of the other 4 who live there? It ends up being a dispute between Abaye and Rabbah. Also: Can an heir to one who dies on Shabbat do that renouncing on Shabbat, and thereby allow an eruv for the neighbors on the courtyard? What is the status of the beneficiary - an extension of the person who died, or a different status altogether? A general principle - that goes beyond the case if the heir: something prohibited before Shabbat is prohibited for all of Shabbat, and something that was permitted before Shabbat is permitted for all of Shabbat, with the exception of renouncing rights to the courtyard. What if one does give up those residential rights on Shabbat? Whether an heir or not. How does this inheritance case relate (if at all) to cases of shelichut - where one takes the place of another?