An eiruv tavshilin is made before Yom Tov in order to allow for cooking for Shabbat on Yom Tov.
However, once I told someone I was worried I had not made my eiruv tavshilin correctly, and the person said, "We rely on the rabbi to make it" (=we don't have to make it ourselves). (This may be because we were both single women, but please ignore that consideration in answering my question.)
Is this true? What extent of shlichus/yotzeius(?) applies to eiruv tavshilin, in general? I assume only one family member per household has to make it. But could it be done, for example, by the rabbi for the whole community? When can we assume that it was done this way?
Discussed to some extent in answers here: If you forgot to make an Eruv Tavshilin