"Always leave the campground cleaner than you found it."
In all my years as a software developer, the only times I've ever gotten to start from scratch is when I've worked on personal projects. And even then, starting from scratch is a last resort.
My experience of being a programmer is working in someone else's architecture. I get to expand it out, fix it up, and sometimes refactor it away. And each time I end up having the same question - why is it built that way? And each time there's the same answer - it's because the code needed to be delivered quickly.
It feels at times that all we can do as programmers is try not to make things worse. One thing I've done is tried to fit in with the existing way of doing things. That way the code is consistent for those who maintain it in the future. But it doesn't solve the problem, merely prevents it from getting any worse.
The answer is meant to be refactoring, though it's really not an answer for fragile code. It's a sad irony that the code in most need of refactoring is the code least able to be refactored...
Any complex system is going to seem impenetrable at first glance, but there are ways to improve it. A system doesn't need to be overhauled to be fixed, and something as simple as tidying up the code that's being worked on is enough to make things better.
For this project, we have pretty abysmal unit testing. So one rule we've set for ourselves is to put unit tests in wherever we find ourselves enhancing the code. Coverage is still woeful, but it is less woeful than it was a month ago. Another thing is to make sure no commit has commented-out code.
Code doesn't get to a messy state by a single act, nor can it be fixed in one. The complex mess that is the average codebase (at least average from my experience) is the way it is because of a long path to that state. Making things better is a similarly long path, but thankfully one that be addressed as part of enhancing a system. Fragility is quantitative, not qualitative.