I agree with what everyone had to say about the consequences of a budget cut. However, I believe that is it very important to understand why the budget is being cut. If it is an overall organizational cut then as mentioned above, the project manager need to evaluate how the budget will be reassigned regarding what is left to carryout a successful overall project. Key changes has to be made in terms of prioritization and documentations. I found this link to be useful in listing exactly the most important steps to be made in such situations.

https://www.lynda.com/articles/10-things-project-budget-cut