I've never had that problem...but I can see it happening. What I do is I make sure my large zigzag stitch is mostly ON the applique and just the needle hole of the other side is on the fabric.This way the hole on the applique is over inside the applique piece and therefore away from the edge so it can't fray the edge. It also covers the whole applique piece edge...so again, the piece is covered and less apt to fray and with one hole off the applique piece and on the fabric...it encloses the applique edge all around. I don't use a "solid", really close ZZ as I want to make sure each hole makes its own indentation and not so close that the two holes merge together. And I always use the widest ZZ the piece will allow..the more stitches the better structure.