I too found that those borders often shrink. That's why I often use an embossed area to place my enbroidery on, either as an oval shield with border or a cross hatched area roughly the shape of the embroidery and slightly larger; the latter works well on fake fur too.
I have found that by embroidering on the tightly woven band on the towels it shrinks when washed I found it better to stitch on the towel itself hugs Shazells****