Feed a Cold; Starve a Fever
How true is the claim? Maybe a bit. A 2002 Dutch study involving just six subjects found that overnight fasting did increase the number of cells that help fight off fever-related bacterial infections, such as the flu. And people who had a meal showed an increase in the cell types that attack cold-related viruses. While the results are intriguing, the experience of only six people in an uncontrolled study doesn't make for sound medical advice.
Why it gets repeated: It's not clear why this tale persists, although you might not feel like eating when you're racked with a fever.
Bottom line: Don't change what you eat on the basis of this adage. Eat sensibly to keep up your strength, and drink plenty of fluids to stay hydrated and to thin congestion-causing mucus.