“All of you” and an inheritor TB Eruvin 70

On today’s daf TB Eruvin 70 two clarifying questions concerning the eruv hatzerot are entertained. “Abaye raised a dilemma before Rabba: If five people live in the same courtyard, and one of them forgot to join in an eiruv, when he renounces his rights in the courtyard, must he renounce them in favor of each and every one of the others or not?” (Sefaria.org translation) Rabba answers him succinctly, “Rabba said to him: He must renounce his rights in favor of each and every one.” (Sefaria.org translation)Apparently Abaye disagrees with his teacher and believes that the person who forgot to join the eruv needs to renounce his rights just to one person and not everybody in the courtyard. Rambam, the Tur[i], and the Shulkan Arukkh decides in favor of Rabba’s position. The one who did not participate in the eruv has to renounces his rights in favor of each and every one of them. The Tur and the Shulkan Arukkh decide that it is sufficient when the person renounces his rights to the people of the courtyard using the plural form of you in Hebrew (וי"א שדי שיאמר רשותי מבוטל' לכולכם)[ii]. (Orekh Hayyim, 380:1)

The second question concerns an inheritor. “Rava raised a dilemma before Rav Naḥman: With regard to an heir, what is the halakha regarding whether he may renounce rights in a courtyard? If a person who had forgotten to establish an eiruv died on Shabbat, may his heir renounce his rights in his stead?” (Sefaria.org translation) Does the death of the person signify a break in ownership and the heir immediately does not have the same rights as the deceased or is the inheritor just a continuation of ownership that is transferred seamlessly?

“The Gemara explains the two sides of the question: On the one hand, perhaps only in a case where, if the person wanted to establish an eiruv on the previous day he could have established an eiruv, he can also renounce his rights on Shabbat. But this heir, since, if he wanted to establish an eiruv the previous day he could not have established an eiruv, as he was not then a resident of the courtyard, therefore, today he cannot renounce his rights either.

“Or perhaps an heir is like his father’s foot, i.e., he is considered an extension of his father and substitutes for him in all regards, which means that just as his father could have renounced his rights, so can he.

“Rav Naḥman said to him: I myself say that an heir can indeed renounce rights in a courtyard, while those scholars of the school of Shmuel taught: He cannot renounce rights in a courtyard.” (Sefaria.org translation)

 Just like in the previous question, now Rava disagrees with Rav Naḥman’s position a tries to prove that the halakha is according to the school of Shmuel. The Shulkan Arukkh poskins that an inheritor may renounce rights in a courtyard. (Orekh Hayyim 381:6)

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[i]  The Tur is an important Halakhic code composed by Jacob ben Asher (Cologne, 1270 – Toledo, Spain c. 1340, also referred to as Ba'al Ha-Turim). The four-part structure of the Tur and its division into chapters (simanim) were adopted by the later code Shulchan Aruch. This was the first book to be printed in Southeast Europe and the Near East. (https://en.wikipedia.org/wiki/Arba%27ah_Turim)

[ii] Hebrew like many foreign languages distinguishes between singular masculine/feminine you (לך) and plural masculine/feminine (כולכם-masculine form of “all of you”)