The cut ends of grograin ribbon unravel.
If the ribbon is very narrow, tie a knot in it and brush the ends with fray block, fray check, or nail polish.
If the ribbon is wider, as far as I know, if you do not want to use fray block, fray check, or nail polish, then "hemming" the ends of the ribbon is the only thing I can think of to stop the unraveling.
Cutting a ribbon at an angle will slow down the unraveling, but will not stop it.