In troubled projects, where extra money comes from really depends on the structure of the contract and the parties' goals. In this case it sounds like the clien

In troubled projects, where extra money comes from really depends on the structure of the contract and the parties' goals. In this case it sounds like the client is asking for specific things to be done that weren't in the original contract, and is offering to pay for them, because the client wants things done ASAP and thinks this will help get the project un-stuck. The client could instead stick to the original contract and attempt to enforce any provisions in it about nonperformance/delays/etc. But that gives the client less ability to directly specify what measures to take now. (This kind of thing happens in private-sector contracting also, e.g. in relationships between oil firms and platform maintenance companies.)