I overcast the cut ends before washing either by serging or sewing a narrow zigzag stitch. Takes a lot less thread using the narrow zigzag stitch. I have an older Pfaff and I use about a 1.5 to 2 widtth and a 2.5 to 3 length.
As butterflywing says, this step definitely minimizes fraying. Keeps the washing machine and dryer neater, too.