A StyleForum user named Orgetorix recommended this method for repairing a pulled thread in silk. He says it’s worked for him a number of times… the next time I’m going to try this before I throw away a tie with a conspicuous pull.
Here’s a technique I’ve used with success to fix pulls in silk: Thread a fine needle with normal thread like you’d use to sew on a button. Don’t wax it or anything—you want some friction. Using a magnifying glass if necessary, try to stick the point of the needle through the silk fabric at the exact point where one end of the pulled thread comes out. You’re trying to get it through the same “hole” in the weave. Pull the needle and thread through to the other side of the fabric and all the way out. If you’re lucky, the friction of the thread passing through the hole will take the pulled thread with it and pull it to the back of the fabric where it’s unseen.
Hope this makes sense. It’s worked for me on various silks, mainly on ties.