If the code is brittle to change, it must not have been particularly safe in the first place, right?

And if it's well-tested, maybe that condition is achieved by the use of a test suite which could verify the changes are safe too?

A test will never catch every bug, otherwise it's a proof, and any change has the probability to introduce a new bug, irregardless of how careful you are. Thus, changing correct code will eventually result in incorrect code.