The only time I have ever seen a problem with fabric, it wasn't that old. A friend had purchased a thin black at a bargain US shop (when our $$ was better) She was making a log cabin and using the black as the centre and when she started to hand quilt it, she noticed a small tear in one piece. She took her nail and rubbed it over a few of the pieces and they started to shred. She painstakingly hand appliquéd a new better quality black square over this and removed the offending pieces.
I have many older pieces in my stash, but if I'm doing all hand work, I try for the best quality I can, preferring to save the thinner fabrics for all machine work.