The phrase "to fall on" means to be responsible for or bear the consequences of something. It can also mean to happen upon, encounter or come across something by chance.
His approach ensures that you have a message that doesn't fall on deaf ears, accelerates buying decisions, and helps you and your clients focus on value vs. price. (inc.com)
In the incident of the death of the insured, such a plan will ensure the nominees don't fall on hard times and are able to meet all financial liabilities. (aegonlife.com)
Your comments and requests, dear readers, do not fall on deaf ears. (vintagevictuals.com)