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.)

Any major IT consultancy company. Especially those working for the government.

But the modus operandus is standard even for small agencies.

You get to bid for a project. If your bid is anywhere near realistic, there's no way you'll ever get it, because the competition will bid way, way lower.

So you put in a bid that you know will never get the project completed and/or will reduce quality well below what will ever be acceptable. However, the contract will be full of loopholes that will allow you to get away with it. You know that once your in, and once the project is far enough along, the client will have no choice but to pay you extra to do what actually needed to be done in the first place.

No, the client is not getting screwed. Especially when it comes to governments and major corporations, everyone knows this is going to happen. It's just impossible to get the project started for anywhere near the real price tag.

But even on a smaller scale, for instance a web agency with a 20K project, if you put in an honest bid you'll either never get the job or be forced to build crap.

From web shopping carts to bridges, people don't value good engineering and planning. Or at least not until they are confronted with the results of bad engineering and planning.

So there's the original budget and there's reality, and an entire cult of rituals surrounding bridging the huge gap between the two. And it is this ritual in which people on both ends take a considerable percentage of the top, so all the decision makers are vested in keeping this ritual going despite all of the well publicized failures.

If you are a contractor and you're not getting at least 50% more out of a gig than the original contract, you're not playing the game very well.

I wonder if these kind of contract arrangments are just a consequence of lack of communication. You have to agree on a single cost because it is impossible to audit and check everything the contractor does. But the client will inevatably have to check everything anyway but in a delayed fashion. So why not assume from the outset that the client is just another part of the team and must sign-of on everything every single day. Give the client complete access to all data about the project. With sufficient communication the contractor could prove they are working correctly and the client justs pay them for the time and materials they use.

Not because we weren't doing our job, but for example I've been involved in cases where we've had to say "I'm sorry, but there is no way we can hit the deadline without more hours and external resources", and client says "fine, here's some more money, just make sure you hit the deadline"