One thing I learned from consulting is if you position yourself as the "fix your mess" guy you have to be very defensive. Ask for more up-front, and bail at the first sign of underpayment.
Be pleasantly surprised when a poorly run project is being run by nice, honest people. Prep for the opposite.
You're not just delivering expertise, you're stepping into a situation where incentives are already misaligned, expectations are fuzzy, and there's often a cashflow problem hiding somewhere
It sounds counterintuitive but from my experience it are often nice and (somewhat) honest people. They just came after whoever messed it up horribly in the first place and at some point they came to the conclusion that they need some external help.