You inherit a 2,000-line legacy module with no tests and must change it. How do you proceed safely?

Read and map the behavior; find the area you must change and its seams.
Add characterization tests that capture current behavior (even strange behavior) around that area.
Refactor in small steps that do not change behavior: extract functions, rename, inject dependencies.
Make the change with tests in place; consider a feature flag.
For big rewrites use the Strangler Fig pattern: move pieces to new code gradually.
Ship in small increments, monitor, keep commits reviewable.