It depends on how far over budget we’re projected to go and how much budgeted dev time we’ve got left. If our [burn rate] is trending way too far over budget to feasibly make our release, the answer is usually “cancel the game”. On rare occasions, when the stars align and the proposal is accepted, the answer is “get the people funding the project to inject additional funding for development time”. Requesting additional funding must be justified, and it’s entirely possible that the additional funding request gets denied and the project ends up either having to make due or gets cancelled.
The most common answer, however, is “Begin cutting features and content from the lowest priority upward until we’re back on budget”. Even if we manage to get additional funding, it is extremely common to cut stuff on top of that to help reassure the publisher that we’re doing our part to control the scope of the project. If we’re lucky, sometimes these lower priority cut features and content can be repurposed into DLC later depending on how much additional work they need. Otherwise, it gets shuffled off to the archives, likely never to be seen again.
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