My understanding is that Unit Tests are intended to protect you while refactoring. Refactoring is not intended to change implementation or purpose, it is intended to restructure without such changes. As such, Unit Tests should (pretty much) never be broken by true refactoring.

Enhancement, improvement and extension are all likely to break Unit Tests, because they can easily require that you change the way things currently work. In this case end-to-end tests are what you need, to make sure your system is producing the right results, including the new enhancements, but especially including the previous results.

In my experience, you can't make substantial improvements to a system with all Unit Tests in place and untouched.

Equally in my experience, with comprehensive Unit Tests you can refactor without fear, and constantly ensure your code is clean and ready for the next phase of development.