Sickly plants are more susceptible to infection than healthy vigorous ones. Just as we throw leftover food away, we should pull up and throw away seasonal plants that are in decline. By leaving them we allow pests a place to set up house and begin an infestation. Once pests find a host plant they often use that plant during their dormant cycle, too. Diseases and insects harbor in decaying organic matter during their dormant cycle.
Sanitation is a simple way to eliminate pest problems.
Sanitation is especially important if you are trying to grow organically. If the foliage of your cool season vegetables or flowers is yellowing, you should prepare to discard them. Pulling the plants out, roots and all, is ideal. Many pests harbor and feed on the portion below ground. Your plant discards can be used to make compost.