All the persons with Owners and Human Resources user roles, and the evaluator can be notified when a pending signature request is processed. You can enable these notifications under Admin Tools > Settings > Notifications and enable the toggle “Notify Owners, HR, and Evaluators when signature requests are processed.”
A person can enable these notifications just for himself/herself by clicking on their picture on the top right corner of the screen, selecting Notifications option and enabling the option “Receive an email when signature requests are processed.”