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My bachelor buttons have a couple with stems looking... alright, but the leaves have wilted and twisted. I have always wondered, If I chop the plant at the soil level, will the roots keep working and build up a new stem? Or is that the death of the plant due to nothing catchign the sun?
After reading your question, I decided to do a little searching online. Although I haven't read anything yet about the condition you say your plants are in (could be a whole different problem...insects or disease?), but I found several sites that say if you cut off Bachelor Buttons "right to the ground" after blooming, it encourages them to rebloom. With a healthy plant it apparently is good for it, but again, I can't say if yours are healthy.
If you can take a picture of one of them and post it in the "Garden Pests and Diseases" forum, there might be someone who could give you more info.
If by Bachelor's Buttons you mean Centaurea, cyanus, cutting them to them ground encourages new growth so I would go ahead and cut away anything you don't like. Do they do that every year?