The application handled a process the business could not invoice without. It had been built by one developer, extended by a second firm, and abandoned by both. There was no documentation, no test environment, and nobody left who could describe how it worked.
Two vendors had already quoted a full rebuild. Neither could say what the existing system did in enough detail to replace it safely.
Repair before replace. A rebuild was the more expensive answer to a problem nobody had diagnosed yet, so the first week went to reading the system rather than pricing its replacement.
The application was stable and in production six weeks after we took it over, with the business running on it and a documented path for what happens next.
One week, fixed fee, written findings, and a straight answer about whether we are the right people for this.