Consider fabrics in which every warp (and weft) strand passes over and under at least \(k\) weft (warp) strands. There is a \(4k\) by \(4k\) fabric of this kind that does not hang together. We prove that any \(n\) by \(n\) fabric of this kind, where \(n< 4k\), does hang together. Moreover, we introduce a measure of how well a fabric hangs together, by defining the strength of a fabric, and two theorems are proved that extend the preceding results.