There could be a few problems here. If the fabric was from the end of the mill run, it had been stretched to the inth degree and now that it has had a time to relax of course it will ravel a bit.
If the fabric had been in the store for a while could be another problem. Handling, moving, humidity, lighting and the like will cause problems over time.
Whenever I've had this happen I find that if I starch the fabric heavily and then iron with a dry iron helps this problem. I use the old fashioned liquid starch and mix my own so that I can control the strength. For something like this I would use a 50/50 mix. You can find it in the laundry section and it's in a blue bottle.
I would seriously doubt that if you put it in a quilt that the quilt will fall apart. You have to remember that your seams will be covered by batting and backing and the quilting will also help relieve the stress on the seams.
I am not affiliated with JoAnn's. Yes you can find inferior fabric as well as quality fabric. No matter WHERE you shop you will find different qualities of fabrics.
Hope this helps.