Here is a link to a video on youtube by Julie at Sew Weird designs. It's a bit more work but it does work well. I too love FSL. Good luck with your projects. Hugs. Nan W
I have had this happen to me. Such a disappointment. I then started using chiffon-type fabric that coordinates with the color and the design, placing it on top or between 2 layers of water soluble fabric for a perfect stitch out. After removing the water soluble fabric with water, use a steady hand and a wood burning tool and you can carefully burn away any fray edges.
I make sure I purchase good quality FSL designs and hoop 1 layer of Badgemaster WSSS then put another piece where the design will be stitching out to be sure all is stable. Just wet each edge and stick it to the other piece. I seldom have trouble doing it this way. But experiment with the different ideas to find what works best for you and your machine.
The only other thing to try is either more stabilizer or less and the type. One sheet of badgemaster is equivalent to 3 sheet of regular solvy. There is a mesh wss that is supposed to be even more stable for FSL, and comes under 2 brands names, both which escape me at the moment. I have used 2 sheets of badgemaster, which does not rinse out well of a really dense FSL piece.