Yep, so-called permanent fabric adhesives are never permanent. I often see surprise on people's faces whenever they use "industrial strength adhesive velcro" and then it falls off within a day of sticking it to their costume.
Those turned under hems will very likely come out after a few wears and washes. Sewing is the only true permanent way to keep them turned in. Also, that adhesive tape will do nothing to prevent the fabric from fraying.
Fray Block can help prevent fraying, but I wouldn't even try it on that vest, to be honest. Everything's already turned under with the tape, so there's a very high chance that the Fray Block would spill over or bleed through the "hem" allowance and into the garment surface area. In my experience, Fray Block leaves a stain mark on most fabrics, so a messy application would be really obvious and ruin the garment.
If the fabric is thick enough, you might be able to get away with applying Fray Block with a throw-away paintbrush for more control. Otherwise, bring a small pair of scissors to snip off the loose fibers as they pull out.
FF9 cosplay? Hit me up!
2013: Anime Los Angeles, Anime Conji
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