Shopify doesn't have a parent -> child theme system in the same way that other platforms like WordPress do. So when you're updating and modifying themes you'd take a different approach. One reliable way to manage updates safely is to use the Shopify GitHub integration to:
Automatically pull and push theme code from any organization or repository associated with your GitHub account
Connect one or more branches from a repository to easily develop and test new theme features or campaigns
Keep a theme up to date with commits to a branch, and track edits made in the Shopify admin, including the code editor and theme editor
Connect branches to unpublished or published themes
To ensure that changes that you make are not affecting your live store, you'd edit a duplicate of the theme and then once you're ready you can publish that duplicate.