To keep cut off jeans from fraying, hem them or fuse interfacing to the back of the denim. The hemming method requires an extra seam allowance.
To hem cut-off jeans, cut them 1 inch longer than the desired length, turn them under 1/2-inch twice, then use a machine to sew the hem. Sew slowly across seams because quickly hitting a thick seam can break the needle and damage the machine.
Fusible interfacing can be ironed to the back of the denim, or any woven material that frays easily, as a no-sew option to stop fraying. Use fusible interfacing tape with glue on only one side. Like an iron-on patch, this might need to be reapplied after a few launderings.
Step 1: Cut the jeans and interfacing
Cut the jeans off as desired. Cut the interfacing long enough to go all the way around the hemline.
Step 2: Pin the interfacing in place
Turn the jeans inside out and pin the interfacing on the exposed underside of the denim, right along the cut edge.
Step 3: Iron the interfacing to the denim
Put a tailor's ham or folded towel inside the leg hole and use a hot iron, on the cotton setting, to press the interfacing to the jeans. Turn the jeans as needed. Allow the interfacing to cool to lukewarm before removing the pins. Press the leg opening again if the interfacing looks loose.