What is the substance produced by the liver that is necessary to break down fat drops into smaller fat droplets

Bile or gall. Bile is produced by the liver and stored in the gallbladder where is going to be concentrated so it can have a stronger power on its action. The bile works as a detergent emulsifying the ingested fat turning it into small droplets so that they can be handled more easily by the lipases - the enzymes that break down fatty acids for absorption.