A google scholar search turns up numerous papers on testability, including models for computing testability, recommendations for how ones code can be more testable, etc.

They all come with the assertion that more testable code is more stable, however I can't find any studies which actually demonstrate this.

I tried looking for studies evaluating the effect of testable code vs. quality, however the closest I can find is Improving the Testability of Object Oriented Systems, which discusses the relationship between design flaws and testability.

Is testable code is actually more stable? And why, or why not?

Please back up your answers with references or evidence to back up your claim.