When I buy over 1 yard of fabric, I wash it in the machine and depending on the season I either hang it outside or run it through the dryer. When it goes through the dryer there are some frays. I get out my handy dandy iron and scissors and I clip off the loose "hairs" when I am ironing, fold it such that loose ends are folded to be covered. When I am going to use the fabric, I iron the creases out again and away I go. Small pieces like fat quarters, no, I do not wash them. I have never had anything fray on me after it was sewed together. I have (excuse me and I am not sorry to say, never come across a smelly piece of fabric. Some were my mom's, some I bought by the bag at our local craft store and I don't know where they have been, but I cut and sew them anyhow and when it is done and ready I wash it. I use my color catcher and I use a Mrs. Meyer's Lavender fabric sheets (they are expensive so I only use them on new quilts) and I have never had a problem.
To Barb - I would never wash a quilt top if it wasn't complete with batting, backing, binding, tying down or machine quilted. That's why all the fraying on the top part of the quilt.
I guess it is a matter of how we are all taught, by classes, by grandmas, by mothers. It is an individual thing I guess. But I can surely see the fraying with 1/4" of hem. I wouldn't take a chance with that kind of a treasure. I'd rather do the whole thing and get it completed and then wash it. If it doesn't work out, it can be used for one thing or another.
But I am glad you kept it. A mother's work is priceless. Edie