For that project I had to make little burlap jewellery bags. Before I came up with the solution of pulling away first one vertical thread and then cut my fabric and then sew the edges to secure it from fraying, I tried to cut directly the piece of the fabric and then fold it and just sew the edges. Without securing it first and without turning the inside out. The result of that is shown below.
The top edges of the bag are fraying and the shape of the bag itself is more square-like than the actual shape of a jewellery bag with round edges etc. For that test I used for the drawstring a bamboo skewer to make a hole in the casing area. I pushed the fibers aside to make the hole; that was something that made worse the fraying problem. I used burlap twine for the drawstring here which I liked best (as it is the same material as the fabric) for my final bags but I was afraid facing the same problem with fraying as burlap twine is thicker than the waxed thread that I eventually used and that would push the threads of the burlap fabric away. I am uploading photos of my final bags to see the difference.