Answer: This time of year most all tender leaved plants dry up. Basil is an annual and will probably not come back next year, at least not from the roots. It's possible, if you let the plant go to seed, that the new seed will germinate in the same place and you'll have a new basil plant next spring, but I wouldn't count on it. You should pull the remains of the plant out of the ground now and remove all debris from the garden plot, to avoid leaving a site for overwintering insects and diseases.
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