From: Rabbi Akiva Eiger
To: Unknown recipient
When a tzuras hapesach breaks on Shabbos in a narrow alleyway, Rabbi Akiva Eiger argues the remaining poles may serve as valid eruv posts: either because inclusion in the original wall constitutes sufficient prior reliance, or because alleyways without houses opening onto them have courtyard status and courtyard posts require no prior reliance at all. He rejects the ho'il ve'hutra avenue as foreclosed by the Shulchan Aruch (OC 363:11), leaves open whether the poles must be a tefach wide, and rules definitively against the correspondent's reading of the Makor Chaim, affirming the Magen Avraham that both sides of a tzuras hapesach require dedicated poles.
Source: Shu"t Rabbi Akiva Eiger §35