Yosef Karo

“ We do not sleep underneath it. Rem"a: This is specifically if it goes along the entire length of the sukkah (Rabbeinu Yerucham) or if it is big enough to insert the head and the majority [of the body] . But otherwise, it is permitted, as there is no sukkah that does not have holes (R"an) . This idea that four of invalid schach or three of open space invalidates a sukkah is specifically when the sukkah is divided into two, and there does not remain a valid measure for a kosher sukkah with walls in one side. ”

“ Therefore, if a house was breached in the middle, schach was placed at the breach, and the ceiling remaining surrounding the valid schach was less than four amot, it is kosher. However, we do not sleep underneath when it is more than four tefachim [wide] . ”