TDD is really commonly misunderstood to be a testing strategy that helps reliability- it's not. It's supposed to guide your software design
That's just writing a regression test and making sure it catches the regression. What does that have to do with TDD? Does the philosophy of TDD lay claim to any test written before the bugfix, regardless of how much or little someone subscribes to TDD overall?
It can provide high level guardrails confirming implementation correctness that are as indifferent to software design as possible (giving freedom to refactor).