As far as I understand it, an עירוב (for carrying on Shabbat) works because it turns the whole area within it into one big רשות היחיד. Now if this is the case, do the laws of רשות היחיד for נזיקין apply (as opposed to the laws of רשות הרבים) when you're inside an עירוב? If so, how would that play out (for example, whose רשות is the area in the עירוב considered to be and how does that affect דיני נזיקין)?
Apparently not. See Bava Kama Daf 81a - certain areas are out of bounds during part of the year only - and entering them then constitutes damaging them.
For Shabbat they retain the same status all year round - probably a Carmelis.
BTW: In Shabbat Dat 6b we see areas they can be private domains for Shabbat and public domains for Tuma.