staystitching is a stabilizing technique for curves in garment sewing. It helps but does not "prevent" anything, esp squareness or stretching. In quiltmaking, I would cut boarders on the straight of grain and measure accurately. You can stay stitch around the edge, using a walking foot, but the binding and/or final measurement has to be taken though the middle of the quilt and the edges eased or stretched to maintain that measurement and thus the squaresness of the quilt which may be pulled out of squareness by the density of quilting among other factors.