Does a rebuild of a base image affect future pulls of a descendant image?

My docker image (which uses the debian base image) runs automated builds on code changes to a git repository. I know that committing to the repository triggers a rebuild, and that each rebuild uses the latest base image available. Are future pulls of my image affected if the base image changes (e.g. Debian rolls security updates), even if my own code does not change (and a rebuild of my own image is not triggered)?

Stated differently, is an image “monolithic” between rebuilds, even if its base image is rebuilt? Or, are changes to a base image reflected in future pulls of its child images? If the former, is this the problem that repository links are intended to solve?

Thank you! Forgive me if this is already answered elsewhere, I am new.