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Yes, it's a tricky question, in my opinion. If it seems like the answer is no, then the answer is yes!
My guess is that the thread is pulled with the same force in both directions. That is, if 1% of the distance has been covered, then that percentage will remain covered, no matter how much you pull. During the next time interval, the bug will crawl less, but it will still move forward. And since it's not exactly a material point, the end will be reached.