Eiruvin 5:7-8

Eiruvin 5:7

If a person to the east of his city told his son to make an eiruv for him to the west of his city, or if a person in the west told his son to make an eiruv to the east, if he is 2,000 cubits to his home but the eiruv is farther away than this, he may walk to his house but not to his eiruv. If he is 2,000 cubits to his eiruv but his home is farther away than this, he may walk to his eiruv but not to his house. If a person places his eiruv in the outskirts of the city (in the 70+ cubits outside the city proper), he has accomplished nothing (because it’s still inside the city). If one places his eiruv even a single cubit outside the city limits, he gains on one side and loses on the other (i.e., the eiruv shifts his personal Shabbos limits that much distance in the direction of the eiruv).

Eiruvin 5:8

The residents of a large city may walk throughout a small city (that is completely within their Shabbos boundary) but the residents of a small city may not walk throughout a large city (that is only partially within their Shabbos boundary). If the resident of a large city put his eiruv in a nearby small city, or vice versa, he may walk the entirety of the city plus 2,000 cubits. Rabbi Akiva, however, says that one only has 2,000 cubits from the location of his eiruv.