Diagnosing a Clobbered Refactor

You dispatched three parallel subagents against the same working directory to refactor a shared utils.py module used by all three: one renaming a function, one adding type hints throughout the file, and one removing a deprecated helper from the same file. When they all finished, utils.py was left in a broken, half-refactored state, and one agent's changes appear to have vanished entirely.

1. Explain exactly what happened, mechanically — not "they conflicted," but why a shared working directory produces this specific failure.
2. Would running these three sequentially (not in parallel) have avoided the problem? What would you have lost by doing that?
3. Redesign this so it's both correct and still faster than fully sequential. Be specific about what changes and what doesn't.