Is it easy to sew the stitching back into its proper place?
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Sorry, I can't copy and paste it.
If the jacket is lined, you'd have to open up the jacket lining to do it by machine, but you could do it by hand easily enough- just a basic hand stitch, being careful to not go all the way the way through- you don't want to pick up the lining- then double back to fill in the gaps. Wouldn't be as durable as a real lockstitch, but it would more than fill the purpose of keeping the fill from moving around.