One idea for tackling this is for the employer to say to the employee "We own everything you do 365 X 24, but we will give you exclusions for pretty much anything as long as you identify the side project name and description in writing."

This means that just about all side projects are permitted, but must be identified in writing in advance, and gives the employer the chance to decline to approve, and in that circumstance then the employee can leave if they want.