...is this square. I figured out what happened. The lady who made this square had run out of yarn, tied a knot, and kept on crocheting. With use and washing, the knot unraveled and that is why it started to fall apart in the middle of a square.
The moral of this is: DON'T MAKE KNOTS. And, if you do, leave a long tail, and weave in. If you make a knot and then cut off close to the knot, it will eventually unravel.