if (something) sneezes, (something else) catches a cold

If a person, group, or entity has a problem or experiences a negative situation, a related person, group, or entity will consequently have a worse problem or will experience a more negative situation. If Paris sneezes, Europe catches a cold. Terrorism in France affects security throughout the continent. You need to keep Aunt Mary happy because, if she sneezes, Mom catches a cold, and you know who else will be miserable along with them? Us! If the executive office sneezes, we all catch a cold—in the form of tons more work!